*Y.-r-g- “maintain”

from IELS: rex

  Rex, which is attested only in Italic, Celtic, and Indic - that
  is at the Western and Eastern extremeties of the Indo-European 
  world, belongs to a very ancient group of terms relating to 
  religion and law. The connexion of Latin rego with Gr. orégo: 
  “extend in a straight line” (the o- being phonologically 
  explainable), the examination of the old uses of reg- in Latin 
  (e.g. in regere fines, e regione, rectus, rex sacrorum) 
  suggests that the rex, properly more of a priest than a king 
  in the modern sense, was the man who had authority to trace out 
  the sites of towns and to determine the rules of law.

TP's commentary: 

  or it belongs to a very ancient group of terms having to do with
  navigation which were introduced by invaders arriving from the east 
  into exactly those Western and Eastern extremeties of the IE area 
  because they have a coastline.   

  regio            “region, the point reached 
                    in a straight line”                     Latin
  e regione        “at the straight point, opposite”        Latin
  regio            “the point reached by a straight 
                    line traced out on the ground
                    or in the sky,
                    the space enclosed between such
                    straight lines drawn in 
                    different directions”                   Latin, in the 
                                                            language of augury
  rectus           “straight as the line which 
                    one draws”                              Latin, in the 
                                                            language of augury
  regula           “the instrument used to trace
                    the straight line”                      Latin, in the 
                                                            language of augury
  regere fines     “trace out the limits by
                    straight lines”                         Latin, in the 
                                                            language of augury

  This is the operation carried out by the high priest before a 
  temple or a town is built and it consists in the delimitation 
  on a given terrain of a sacred plot of ground. The magical 
  character of this operation is evident: what is involved is 
  the delimitation of the interior and the exterior, the realm 
  of the sacred and the realm of the profane, the national 
  territory and foreign territory. The tracing of these limits 
  is carried out by the person invested with the highest powers, 
  the "rex".


  Opposed to the "straight" in the moral order is what is “twisted,
  bent”. Hence "straight" is equivalent to "just", "honest", while 
  its contrary "twisted, bent" is identified with "perfidious", 
  "mendacious", etc.

  I should be very surprised if that crookedness is not related to 
  that horrible serpent, *H-n-g-, again.

  This set of ideas is already Indo-European. To Latin 'rectus' 
  corresponds the Gothic adjective 'raiht-s', which translates 
  Greek 'euthús' “straight”; further the Old Persian 'ra:sta' 
  which qualifies the noun 'the way' in this injunction: 
  'Do not desert the straight way'.    

  raja              “king, prince, lord”                     Sanskrit
  ravi              “sun”                                    Sanskrit
  raj               “to shine”                               Sanskrit, also 
  rajas             “space”                                  Sanskrit, from 
  raj               “to spread out, stretch”                 also 
  loka              “world, space, people”
  rajas             “energy, activity”                       Sanskrit
  raj               “to rule”                                Sanskrit

IENH 428:
  *?[a|ë]r-ag-      “to climb on, to mount; 
                     to rise, to be lifted up; 
                     to lift up, to raise”                   Proto-Nostratic >
  *(e|o)rg[h]-      “to climb on, to mount; 
                     to rise, to become puffed up”           Proto-IndoEuropean
  *?org[h]i-        “testicle” (< “puffed up, swollen”)      Proto-IndoEuropean
  *?[a|ë]r[a|e]g-   “to climb on, to mount; 
                     to rise, to ascend”                     Proto-AfroAsiatic
  *ark-             “to climb, to mount an animal, 
                     to rise, to get puffed up”              Proto-Dravidian
  ergü-, örgü-      “to lift up, to raise”                   Mongolian
  ürgü-             “to lift”                                Buriat (Alar  dialect)               
  ïrge-             “to lift”                                Buriat (Khori dialect)

IENH 591:
  *r[a|ë]k'-        “to stretch, extend, draw out”           Proto-Nostratic >
  *r(e|o)k'-        “to stretch, extend, draw out”           Proto-IndoEuropean
  *r[a|ë]k'-        “to stretch, extend, draw out”           Proto-AfroAsiatic
IENH 599: 
  *r(a|ë)q'-        “to observe, watch, 
                     regard attentively;
                     to supervise, control”                  Proto-Nostratic >
  *r(e|o)k'- (lengthened grade *r(e:|o:)k'-)
                    “to observe, watch, 
                     watch for, care for”                    Proto-IndoEuropean
  *req'-            “to drive (cattle)”                      Proto-Kartvelian
  *r(a|ë)k-         “to observe, watch, 
                     regard attentively;
                     to supervise, control”                  Proto-AfroAsiatic

IENH 600:
  *r(a|ë)k[h]-      “to put together, 
                     put in order, arrange”                  Proto-Nostratic
  *r(e|o)k[h]-      “to put together, 
                     put in order, arrange”                  Proto-IndoEuropean
  *rakkæ-           “to put together, 
                     put in order, arrange”                  Proto-FinnoUgric


  *or-                                                       Proto-IndoEuropean
  *or-t-  participle 
  o:rto             “rose, went up”                          Greek
  ortus (particpl.)                                          Latin
  ortus (noun) (gen. ortu:s)                                 Latin
  art                                                        Middle High German
  von arde (ho:he erborn) 
                    “according to ancestry”                  Middle High German
  ori:ri            “rise, arise, 
                     come into existence”                    Latin
  ori:go            “origin”                                 Latin

  *Y.-r-                                                     Proto-AfroAsiatic
  *Y.-r-d- , -d- corresponding to the Indo-European participial -t-
  Y.arada  (perf.)  “(a plant, a tree, a canine tooth, 
                     a camel's tush) came forth”             Arabic
  Y.arga   (intr.)  “rose, went up”                          Ethiopian
  Y.araga  (trans.) “he ascended, mounted 
                     (the stair, the ladder)”                Arabic
  mi-Y.ra:gun       “a ladder, 
                     a series of steps or stairs”            Arabic

  *or-                                                       Proto-IndoEuropean
  ordo              “row, order”                             Latin
  ordéo:            “start a weaving”                        Greek
  ex-ordior         “start a weaving”                        Latin
  ordior            “order by row, sew, begin”               Latin
  *Y.-r-A , transitive *Y.aráA >
  *re:-                                                      Proto-IndoEuropean
  reju (inf. reti)  “put in order, 
                     place wood in layers”                   Lithuanian
  *ra-,  reduced in participle            
  rodh (fem.)       “row”                                    Old Norse
  rat  (fem.)       “row, line”                              Middle High German
  *Y.-r-                                                     Proto-AfroAsiatic
  Y.a:rakh          “order (e.g. the firewood on the altar),
                     build”                                  Hebrew
  Y.èrækh, Y.ærk-   “ordering into layers”                   Hebrew      
  Y.èrækh, Y.ærk-   “order”                                  New Hebrew
  Y.ari:kha:        “ordering”                               New Hebrew
  Y.erikhu:th       “order”                                  New Hebrew
  *Y.-r-m-  niph.   “be heaped”                              Hebrew
  Y.a:ram           “to heap”                                New Hebrew
  Y.aramatun        “a quantity of reaped 
                     corn collected together,
                     a heap of dung”                         Arabic
  Y.are:ma:         “heap (of cereal, 
                     fruit, rubble)”                         Hebrew
  Y.are:ma:         “heap of cereal”                         New Hebrew
  Y.are:mtha:       “heap of cereal”                         Judeo-Aramaic
  or-g-, org-       “reach, direct”                          Proto-IndoEuropean 
  oréknumi, orégo   “reach”                                  Greek
  *r-g-                                                      Proto-Indouropean
  rego              “direct”                                 Latin
  e:-rigo           “erect”                                  Latin
  rikan             “to heap”                                Gothic
  rogus             “heap (of combustible material), pyre”   Latin
  ra:zajeiti        “points, sets straight, sets in order”   Avestan
  ham-ra:zajeite:   “stretches (himself) out, reaches up”    Median
    with n-infix
  rnjá-ti           “stretches himself”                      Sanskrit
  rakkr             “upright”                                Old Norse
  rekkja            “bed”                                    Old Norse
  *Y.-r-sh- < Y.-r-k-                                        Proto-AfroAsiatic
  Y.ari:s^uN        “wooden structure, tabernacle 
                     constructed of wood and thuma:m herb 
                     (Panicum dichotonum, used by the 
                     Arabs to cover their huts), a booth 
                     or a shed, or thing constructed 
                     for the shade”                          Arabic 
  Y.ars^uN          “a structure of wood built at the head 
                     of a well (forming a shade), the bier
                     of a corpse, a (king's) throne”         Arabic
  irs^u             “bedstead, bed”                          Assyrian
  Y.æræsh           “bed, bier”                              Hebrew
  Y.æræs            “bed”                                    New Hebrew
  Y.arså:           “bed”                                    Syriac
  Y.arsa:           “bed, bier”                              Judeo-Aramaic
  Y.ari:shun        “the elevated structure made for a 
                     grape-vine, of sticks or pieces 
                     of wood”                                Arabic
  Y.ari:sh          “tabernacle, shed for shade”             Ethiopian
  Y.arasha          “he built a building of wood, 
                     he constructed or built what is 
                     called an Y.ari:sh > he built
                     (al-bayta, the house)”                  Arabic
  Y.arrasha II      “he made (al-Garsha), 
                     he roofed (al-bayta, the house)
                     and raised the building (thereof)”      Arabic
            V       “he became settled (bi-l-baladi, 
                     in the country or town)”                Arabic
  Y.-r-s            “put on spalier”                         New Hebrew
  Y.arsela:         “guard hut”                              Judeo-Aramaic

  *H3régs (gen. H3régos) - H3rég-on “ruler, king”
  (gen. ri:g)       “king”                                   Old Irish 
  -rix              “king”                                   Gaulish
  re:x              “king”                                   Latin
  Resos              name of mythic king                     Thracian
  b&r&zi-ra:z       “ruling in the heights”                  Avestan
  kathi-ra:ysa, appr.
                    “mayor” (< “town-ruler”)                 Khotanese
  *raz(i)-puthra >
  rra:s-pu:ra       “prince”                                 Khotanese
  *raz(i)-dugdar >
  rra:s-duar        “princess”                               Khotanese
  ra:j-             “king”                                   Sanskrit
  sam-ra:j-         “overlord”                               Sanskrit

  ri:gain           “queen”                                  Old Irish
  *ri:gani- >
  rhiain            “maiden”                                 Welsh
  *re:gni:-na:- >
  re:gi:na          “queen”                                  Latin
  rra:ysan-         “lord, ruler”                            Khotanese
  rri:na            “queen”                                  Khotanese
  ra:jan-           “king”                                   Sanskrit
  ra:jni-           “queen”                                  Sanskrit
  sam-ra:jni-       “wife of an overlord”                    Sanskrit
  ra:janyá-         “royal”                                  Sanskrit 

  *H3rég-yo-m       “kingdom, power”
  ri:ge             “kingdom”                                Old Irish
  *ra:zya >
  ra:s^a-           “power, might”                           Khotanese
  ra:jyam           “kingdom”                                Sanskrit

  *H3rég-yo-s       “royal”
  re:gius           “royal”                                  Latin
  ra:jyá-           “royal”                                  Sanskrit

  *H3reg-   “move in a straight line; extend, stretch”
  rigid             “stretches”                              Old Irish
  ro(d)i            “gives”                                  Middle Welsh
  rego:             “direct in a straight line”              Latin
  rekja             “stretch, spread out”                    Old Norse
  reccan            “stretch out; be concerned about”        Old English
  reck                                                       English
  rec(c)han         “stretch out”                            Old High German
    (pres. part.)   “reaching out, extending”                Gothic
  rézhti            “stretch”                                Lithuanian
  rie:zt            “stretches up”                           Latvian
  orégo             “stretch”                                Greek
  hargana:u-        “palm, sole”                             Hittite
  kheiros oregnús   “stretching out the hands”               Greek
  ra:zayeiti        “adjusts, arranges”                      Avestan
  rñjati / rjyati   “stretches, stretches out”               Sanskrit
  räk-              “strech out, cover”                      TokharianAB

  *H3regtos “right”
  recht             “law, authority”                         Old Irish 
  re:ctus (adj.)    “right”                                  Latin 
  re:tt-r           “right, law, legal claim”                Old Norse
  re:tti            “direction”                              Old Norse
  re:tta            “rule, land”                             Old Norse
  riht              “right”                                  Old English
  right                                                      English
  reht              “right, justice”                         Old High German
  raiht-s           “right”                                  Gothic
  raihtis (adv.)    “indeed, rightly”                        Gothic
  orektós           “stretched out”                          Greek
  ras^ta-           “right, straight”                        Avestan

  riki              “realm, kingdom”                         Old Norse

  ravi              “sun”                                    Sanskrit
  areg-akn          “sun”,
               lit. “eye of the sun”                         Armenian
  arew              “sun”                                    Armenian

HSED 2088: *ra' “sun, god”
  r´                “sun, Sun-god”                           Egyptian
  *re:              “sun, Sun-god”                           Coptic
  ri                “sun, Sun-god”                           Akhmimian
  re:               “sun, Sun-god”                           Bohairian
  re:               “sun, Sun-god”                           Sahidic
  *rayi- < *raHi-   “sun”                                    West Chadic
  ri                “sun”                                    Geji
  are               “sun”                                    Sha
  *raH-             “sun, god”                               East Chadic
  ra                “sun, god”                               Mokilko
  ra:ya             “sun, god”                               Bidiya
Possibly related to 
  *ray'-            “daylight”                               Semitic
  ray'-             “daylight”                               Arabic
  'ry               “sky”                                    Egyptian
                                                            (Greek papyri)

HSED 2077: *ra?-/*raw-/*ray- “be, become, make”
Consonantal alternation *-?- ~ *-w- ~ *-y-
( TP: or possibly metathesis ?r > r?)
  ìry               “be, do, make”                           Egyptian
                                                             Old Kingdom
  *?iri             “be, do, make”                           Coptic
  ili               “be, do, make”                           Fayumian
  eire              “be, do, make”                           Akhmimian
  iri               “be, do, make”                           Bohairian
  eire              “be, do, make”                           Sahidic
  *ra?-/*raw-                                                West Chadic
  ra                “become”                                 Gwandara
  ro                “work”                                   Bokkos
  *ray-             “become, build”                          Central Chadic
  re, rey           “become, build”                          Lame
  *riy-                                                      East Chadic
  orriye            “become”                                 Dangla
  riyo              “work, make”                             Dangla
  riy               “work, make”                             Bidiya
  Secondary *i before *y.
  *ra?-             “stay, remain”                           Rift
  ra?-              “stay, remain”                           Asa
  raw-              “stay, remain”                           Dahalo

possibly (from the sense “stretch” or “survey”)
HSED  122: *?orah- “road, way”
  *?urah-           “way”                                    Semitic
  ?arhu             “way”                                    Akkadian
  ?o:rah            “way”                                    Hebrew
  ?rh               “way”                                    Aramaic 
                                                            (Emp, Palm)
  ?u:rha:           “way”                                    Aramaic (Syr)
  'whr?             “way”                                    Aramaic (Mand)
  ?urh              “way”                                    Aramaic (NAram)
  *?wara- < *?waraH- “road”                                  West Chadic
  ar                “road”                                   Sura
  ar                “road”                                   Angas
  war               “road”                                   Ankwe
  ?araw             “road”                                   Kulere
*-H- is. probably, preserved as -w- in Klr but lost elsewhere
  *?war-            “road”                                   East Chadic
  ?oora             “road”                                   Bidiya
  An alternative reconstruction could be *waHar- with a
  metathesis and a regular contraction of *-waHa- > Bidiya -oo-
  *?or-             “road”                                   Highland East 
  ora               “road”                                   Darasa
  No traces of the laryngeal
  *?uruw            “path, way”                              Rift
  uruwa             “path, way”                              Gorowa
  Secondary formation in -uwa. The loss of laryngeal in
  Rift is irregular. 

  *yar              “do, make”                               East Chadic
  *ray              “build”                                  Central Chadic
  ìry               “do, make”                               Egyptian

  *rid.-            “do, make”                               West Chadic
  rdy               “do, make”                               Egyptian

  sarge:l           “ruler (tool, not person)”               Hebrew
  regel, ragl-      “foot (body part)”                       Hebrew
  sirge:l           “to draw straight lines”                 Hebrew

  rak               “reach” (of river)                       Dutch
  rekken            “stretch”                                Dutch

  cf. Benveniste above on “rex”
  artam, artms,
  arthem            Artemis, goddess of 
                    spells and prophecy                      Etruscan
  arth              “to section or subdivide”                Etruscan
  arthe velna       “one who severs, cuts off”               Etruscan
  artna             “limb, member, part”                     Etruscan
  artna mem[p]ru    “one who subdivides in parts”            Etruscan
  arta              “breaker, smasher” > 
                    “carpenter (Vulcan)”                     Etruscan
  artile            “one who articulates, artisan”           Etruscan

  ragam             “manner, way, fashion”,
                    “kind, sort, type”,
                    “color”                                  Indonesian
  rakit             “raft; bamboo-floor”                     Indonesian
  berakit           “closely linked (joined)”                Indonesian
  merakit           “connect, tie, join”,
                    “make up, devise, contrive”              Indonesian
  rangka            “skeleton”,
                    “draft, scheme”                          Indonesian
  rangka dada       “thorax, chest”                          Indonesian
  merangkakan       “to design”                              Indonesian
  rangkai           “bunch”                                  Indonesian
  serangkai         “associated, connected. linked”          Indonesian
  berangkai-rangkai “[inter-]connected,
                     linked in a row”                        Indonesian
  merangkai[kan]    “join, connect, link, combine”           Indonesian
  [pe]rangkaian     “connection, link, chain;
                     series, collection;
                     structure, scheme”                      Indonesian

CAD 19.320:
  a:ri              “king, ruler”                            Isnag
  *ha:zi                                                     Proto-Hesperonesian
  ha:ri?             id.                                     Tagalog
  hari?              id.                                     Sarangani Blaan
  ratu               id.                                     Javanese
  ratu               id.                                     Sika
  latu               id.                                     Kwanera
  ari?i              id.                                     Tahitian
  ?ariki             id.                                     Rapanui

  lugal             “king”                                   Sumerian

  rahu-             “king”                                   Philippines
  raha-             “respected married elder”                Arosi
  araha-            “chief, ruler”                           common Melanesian
  rato-             “elder”                                  Solomon Is.
  mae-raha-         “chief”                                  Wango
  rato-             “chief”                                  Arosi
  ratu-             “master, lord”                           Fiji
  ratu-             “chief, noble”                           Java
  latu-             “master builder”                         Samoa
  ra'atira-         “chief”                                  Tahiti
  lakan-            “chief, lord”                            Tagalog
  ma-raja-          “important person”                       Orang Besar
  toma-raya-        “king”                                   Sekol
  datu-             “chief, leader”                          common Philippines, 
  lakas-            “energy, strength, strong”               Philippines
  lakwa-            “quickly”                                Melanesia
  laki-             “great”                                  SE Papuan
  rakahi'a-         “to heat, warm”                          Are'are
  raka-             “to be powerful magically”               Are'are
  raka-             “to make fire”                           Solomon Is.
  laki-             “fire”                                   Motu
  lake-             “fire”                                   Vaturana
  raka              “excessive, overly hot”                  Ulawa
  rakahi-           “excessive”                              Wango
  rakahi-           “to heat, melt”                          Ulawa
  a-raka-           “fire”                                   Suki

  raya              “to be great, large”                     Indonesia
  ra, raa, la-      “distant in space or time”               common Oceanic
  laki-             “largeness”                              Philippines
  lakihan-          “to enlarge”                             Philippines
  loki-             “large”                                  Vaturana
  lagay-            “place, position, fix”                   Philippines
  lugal-            “place”                                  Philippines
  laganap-          “widespread”                             Philippines
  lagalag-          “roving, wandering”                      Tagalog
  latag-            “spread over, extended”                  Philippines
  lata-             “large, wide”                            Marino
  lokwo-            “large, spacious”                        Ngwatua
  lakwoa-           “large, spacious”                        Lolsiwoi
  latlat-           “to spread out”                          Proto-Philippine
  rita-             “to spread out”                          Proto-Malaitan
  reten-            “to stretch out”                         Proto-Austronesian
  ruqan, ruqar-     “space, open space”                      Proto-Austronesian
  rangi, langi-     “sky, heavens, space, wind”              common Austronesian
  lagi-             “sky, heavens”                           Nanumea
  laki-             “man, male”, rarely “mankind”            common Austronesian

  laqi-             “offspring”                              Atayal

  a-lahaa-          “to rule”                                common Melanesian
  lavak (pa-)-      “to rule”                                Paiwan
  ari (mag-)-       “to rule”                                Tagalog

But what is the connection with *l-w-k- “light”?
                            and *H-r-k- “sun, silver, gold, fire”?

Possibly, with a d-preformative:
  *trek(k)a-        “drag, pull” (TP: by two?)               Proto-Germanic
  trechen            id.                                     Middle High German
  treka              id.                                     Old Frisian
  trecken            id.                                     Middle Dutch, Middle Low German
  trek               id.                                     Dutch

Possibly, with an s-preformative:
  *strak[ki]je-                                              Proto-Germanic
  strekkja           “stretch, reach”                        Old Norse
  strecken            id.                                    Old High German
  streccean           id.                                    Old English
  strecken            id.                                    German