95:
85:
64:
1023:. Yes clearly. The only reason there are two articles is due to an old historical, uhh... accident. Creating the other article seemed like the right thing to do at the time. Oh, and I'd leave adjoint bundle alone. Right now, its thin, but I think it could be expanded ... bundles are really quite a different thing; half of particle physics happens on adjoint bundles, and you don't want to start talking about particle physics here, or, at least, not much.
33:
173:
213:
803:, which is currently a disambiguation page. The two concepts are so closely related, they are both defined in the article currently (the adjoint representation of a "Lie group" and a "Lie algebra"), so there is no need for a disambiguation page. Some textbooks define both concepts nearly simultaneously. This has also been discussed at
924:
If Aut(g) are the automorphism of the Lie algebra g, that is linear operators preserving the Lie brackets, does Ad really associates to any element of G an element of Aut(g)? Is it possible that this holds only if G is a group of matrices for which holds the nice formula Ad_x (a) = x a x^(-1), (x is
1087:
In an introduction section where the words "for example" appear, it would be nice to see an actual example. Like here's a 2x2 matrix and it's adjoint. Look at the example that's given here in the 2nd sentence of the article and note how ridiculous it is.
1004:
Yes, if it were done with care, it is the most sensible thing to do. I'm just indicating that, procedurally, since all merge templates refer one to here, it is here, in the Target article, where the formal proposal and discussion should reside.
734:
660:
1060:
Currently all the examples of adjoint representations in Lie groups are abstract. Can somebody provide a few numerical examples please? This would make the concept a lot easier to understand. Thank you! 23 January 2022
1037:
Given the consensus above that this is a good idea, I've moved the text over to about the right place, but haven't efficiently integrated it into the existing summary; some assistance in tidying it would be appreciated.
586:
409:
979:
to here, in the Lie-alg article. As you can see, the materials there mostly overlaps stuff here and there is not much to say about adjoint rep of Lie algebra that appear outside the context of Lie groups.
260:
I really wouldn't say has much to do with it. There is no obvious relation, for a group G, between acting on itself by conjugation and by translation - very different permutation representations.
1068:
151:
285:
I'm coming at this from a robotics/computer-vision perspective. I don't fully follow the Formal
Definition section, but it sounds to me like the adjoint representation of a group element,
825:. The Lie group and Lie algebra points of view seem so closely connected that it makes sense to have a single article that covers both, and the new name better reflects this unity. —
274:
This does not sound right. "representation" can refer either to a vector space with an action of a group or to the group morphism from G to GL(V). Neither of these applies here.
960:). I'd let him do that here.If people did the merge carefully and tastefully, it would look like a good idea to me. (But I might not have the time to contribute to it, myself.)
519:
353:
448:
199:
1116:
141:
666:
592:
976:
527:
804:
117:
1111:
788:
760:
Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a
1089:
936:
1072:
1024:
364:
108:
69:
944:
44:
812:
488:
751:
867:
830:
1093:
940:
956:
I note that Murata-san put up merge templates, but without starting, this, the merge proposal discussion. (
473:
238:
1028:
1010:
994:
965:
886:
800:
792:
189:
17:
909:
808:
761:
263:
50:
94:
1064:
932:
925:
in G, a is in g), whilst in the most general situation G is sent by Ad into linear operators g -: -->
796:
500:
192:
on 19 August 2017. For the contribution history and old versions of the redirected page, please see
32:
863:
826:
246:
293:), is a linear operator that acts on the vector representation of a tangent vector at the origin,
116:
on
Knowledge. If you would like to participate, please visit the project page, where you can join
778:
469:
454:
100:
311:
84:
63:
1043:
1006:
990:
961:
957:
882:
245:
Please help fix the broken anchors. You can remove this template after fixing the problems. |
185:
417:
852:
225:
862:
Thanks, but please note that I am very much not an expert on Lie groups and Lie algebras. —
739:
It's probably obvious if you understand this more than I do. :-) 15:56, 9 June 2011 (UTC)
983:
1105:
774:
1039:
899:
237:] The anchor (#Derivation on a Lie algebra) is no longer available because it was
1097:
1076:
1047:
1032:
1014:
998:
969:
890:
871:
857:
834:
816:
782:
477:
843:
842:
per nom and per David
Eppstein, whose wisdom on this matter I trust implicitly.
113:
908:
Subsequent comments should be made in a new section on this talk page or in a
729:{\displaystyle \left.{\frac {\partial \Psi _{g}(h)}{\partial h}}\right|_{h=e}}
655:{\displaystyle \left.{\frac {\partial \Psi _{g}(h)}{\partial g}}\right|_{g=e}}
90:
986:, I don't see a need for a separate article as opposed to having a section.
581:{\displaystyle \left.{\frac {\partial \Psi _{g}}{\partial g}}\right|_{g=e}}
929:
I'm probably wrong, it has been a while since i've studied this stuff.
233:
This article links to one or more target anchors that no longer exist.
468:
Is that even remotely right? Appologies for imprecise lingo. Thanks.
975:
Certainly. Actually, there was already discussion about merging
404:{\displaystyle \mathbf {s} '=\operatorname {Ad} (g)\mathbf {s} }
457:
from the tangent space of the identity to the tangent space of
207:
167:
26:
672:
598:
533:
521:." Which of these is it referring to (abusing notation)?:
750:
The following discussion is an archived discussion of a
194:
180:
497:
at the identity is an automorphism of the Lie algebra
305:, of the same tangent vector at the origin. That is,
898:
The above discussion is preserved as an archive of a
669:
595:
530:
503:
420:
367:
314:
112:, a collaborative effort to improve the coverage of
764:. No further edits should be made to this section.
912:. No further edits should be made to this section.
728:
654:
580:
513:
487:I'm confused by the sentence "It follows that the
442:
403:
347:
799:, I believe this article should be located at
8:
301:would operate on the matrix representation,
270:Any Lie group is a representation of itself?
198:; for the discussion at that location, see
1062:
277:Better: any Lie group G acts on itself...
58:
18:Talk:Adjoint representation of a Lie group
714:
684:
674:
668:
640:
610:
600:
594:
566:
545:
535:
529:
505:
504:
502:
431:
419:
396:
369:
366:
336:
313:
977:adjoint representation of a Lie algebra
414:up to representation. My sense is that
181:Adjoint representation of a Lie algebra
60:
30:
1069:2603:7000:413F:9456:1128:6028:14AD:F69
1083:Another incomprehensible math article
789:Adjoint representation of a Lie group
7:
769:The result of the move request was:
106:This article is within the scope of
506:
49:It is of interest to the following
1117:High-priority mathematics articles
945:_Aut(g)_for_any_Lie_group_G?": -->
701:
681:
677:
627:
607:
603:
553:
542:
538:
25:
126:Knowledge:WikiProject Mathematics
926:g (not Lie bracket preserving)?
397:
370:
211:
171:
129:Template:WikiProject Mathematics
93:
83:
62:
31:
514:{\displaystyle {\mathfrak {g}}}
146:This article has been rated as
1033:01:45, 18 September 2016 (UTC)
696:
690:
622:
616:
393:
387:
1:
1015:23:32, 16 December 2014 (UTC)
999:22:28, 16 December 2014 (UTC)
970:15:25, 16 December 2014 (UTC)
946:22:32, 11 December 2013 (UTC)
891:01:35, 21 February 2013 (UTC)
872:01:03, 17 February 2013 (UTC)
858:16:31, 15 February 2013 (UTC)
835:18:29, 14 February 2013 (UTC)
817:17:14, 13 February 2013 (UTC)
783:16:10, 21 February 2013 (UTC)
281:Transport of tangent vectors?
120:and see a list of open tasks.
1112:C-Class mathematics articles
1077:04:56, 24 January 2022 (UTC)
465:) is doing a similar thing.
1048:09:12, 19 August 2017 (UTC)
920:Aut(g) for any Lie group G?
348:{\displaystyle S'=gSg^{-1}}
1133:
483:Derivative at the origin?
266:06:43, 23 Aug 2003 (UTC)
145:
78:
57:
1098:10:15, 8 July 2023 (UTC)
905:Please do not modify it.
757:Please do not modify it.
478:15:24, 18 May 2011 (UTC)
443:{\displaystyle gSg^{-1}}
152:project's priority scale
919:Is really Ad : G -: -->
805:WikiProject Mathematics
109:WikiProject Mathematics
801:Adjoint representation
793:Adjoint representation
730:
656:
582:
515:
444:
405:
349:
190:Adjoint representation
39:This article is rated
731:
657:
583:
516:
445:
406:
350:
178:The contents of the
667:
593:
528:
501:
455:parallel transported
418:
365:
312:
132:mathematics articles
1056:Numerical Examples
726:
652:
578:
511:
440:
401:
345:
101:Mathematics portal
45:content assessment
1079:
1067:comment added by
935:comment added by
771:moved per request
708:
634:
560:
358:is equivalent to
253:
252:
239:deleted by a user
228:in most browsers.
206:
205:
166:
165:
162:
161:
158:
157:
16:(Redirected from
1124:
948:
907:
850:
759:
735:
733:
732:
727:
725:
724:
713:
709:
707:
699:
689:
688:
675:
661:
659:
658:
653:
651:
650:
639:
635:
633:
625:
615:
614:
601:
587:
585:
584:
579:
577:
576:
565:
561:
559:
551:
550:
549:
536:
520:
518:
517:
512:
510:
509:
449:
447:
446:
441:
439:
438:
410:
408:
407:
402:
400:
377:
373:
354:
352:
351:
346:
344:
343:
322:
264:Charles Matthews
247:Reporting errors
215:
214:
208:
197:
175:
174:
168:
134:
133:
130:
127:
124:
103:
98:
97:
87:
80:
79:
74:
66:
59:
42:
36:
35:
27:
21:
1132:
1131:
1127:
1126:
1125:
1123:
1122:
1121:
1102:
1101:
1085:
1058:
954:
952:Merger proposal
930:
922:
916:
903:
844:
755:
745:
700:
680:
676:
671:
670:
665:
664:
626:
606:
602:
597:
596:
591:
590:
552:
541:
537:
532:
531:
526:
525:
499:
498:
496:
485:
470:—Ben FrantzDale
427:
416:
415:
368:
363:
362:
332:
315:
310:
309:
283:
272:
258:
249:
231:
230:
229:
212:
193:
172:
131:
128:
125:
122:
121:
99:
92:
72:
43:on Knowledge's
40:
23:
22:
15:
12:
11:
5:
1130:
1128:
1120:
1119:
1114:
1104:
1103:
1084:
1081:
1057:
1054:
1053:
1052:
1051:
1050:
1002:
1001:
987:
984:adjoint bundle
980:
953:
950:
921:
917:
915:
914:
900:requested move
894:
893:
876:
875:
874:
864:David Eppstein
837:
827:David Eppstein
786:
767:
766:
752:requested move
746:
744:
743:Requested Move
741:
737:
736:
723:
720:
717:
712:
706:
703:
698:
695:
692:
687:
683:
679:
673:
662:
649:
646:
643:
638:
632:
629:
624:
621:
618:
613:
609:
605:
599:
588:
575:
572:
569:
564:
558:
555:
548:
544:
540:
534:
508:
492:
484:
481:
437:
434:
430:
426:
423:
412:
411:
399:
395:
392:
389:
386:
383:
380:
376:
372:
356:
355:
342:
339:
335:
331:
328:
325:
321:
318:
282:
279:
271:
268:
257:
254:
251:
250:
244:
243:
242:
226:case-sensitive
220:
219:
218:
216:
204:
203:
176:
164:
163:
160:
159:
156:
155:
144:
138:
137:
135:
118:the discussion
105:
104:
88:
76:
75:
67:
55:
54:
48:
37:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1129:
1118:
1115:
1113:
1110:
1109:
1107:
1100:
1099:
1095:
1091:
1090:98.156.185.48
1082:
1080:
1078:
1074:
1070:
1066:
1055:
1049:
1045:
1041:
1036:
1035:
1034:
1030:
1026:
1022:
1019:
1018:
1017:
1016:
1012:
1008:
1000:
996:
992:
988:
985:
981:
978:
974:
973:
972:
971:
967:
963:
959:
951:
949:
947:
942:
938:
937:93.50.121.192
934:
927:
918:
913:
911:
906:
901:
896:
895:
892:
888:
884:
880:
877:
873:
869:
865:
861:
860:
859:
856:
855:
851:
849:
848:
841:
838:
836:
832:
828:
824:
821:
820:
819:
818:
814:
810:
806:
802:
798:
797:WP:CONCEPTDAB
794:
790:
785:
784:
780:
776:
772:
765:
763:
758:
753:
748:
747:
742:
740:
721:
718:
715:
710:
704:
693:
685:
663:
647:
644:
641:
636:
630:
619:
611:
589:
573:
570:
567:
562:
556:
546:
524:
523:
522:
495:
490:
482:
480:
479:
475:
471:
466:
464:
460:
456:
453:
435:
432:
428:
424:
421:
390:
384:
381:
378:
374:
361:
360:
359:
340:
337:
333:
329:
326:
323:
319:
316:
308:
307:
306:
304:
300:
296:
292:
288:
280:
278:
275:
269:
267:
265:
261:
255:
248:
240:
236:
235:
234:
227:
223:
217:
210:
209:
201:
200:its talk page
196:
191:
187:
183:
182:
177:
170:
169:
153:
149:
148:High-priority
143:
140:
139:
136:
119:
115:
111:
110:
102:
96:
91:
89:
86:
82:
81:
77:
73:High‑priority
71:
68:
65:
61:
56:
52:
46:
38:
34:
29:
28:
19:
1086:
1063:— Preceding
1059:
1025:67.198.37.16
1020:
1007:Cuzkatzimhut
1003:
962:Cuzkatzimhut
955:
931:— Preceding
928:
923:
904:
897:
878:
853:
846:
845:
839:
822:
787:
770:
768:
756:
749:
738:
493:
486:
467:
462:
461:, and so Ad(
458:
451:
413:
357:
302:
298:
294:
290:
286:
284:
276:
273:
262:
259:
232:
224:Anchors are
221:
179:
147:
107:
51:WikiProjects
910:move review
762:move review
195:its history
123:Mathematics
114:mathematics
70:Mathematics
1106:Categories
958:WP:Merging
489:derivative
184:page were
1065:unsigned
933:unsigned
775:Favonian
297:the way
256:Untitled
1040:Klbrain
982:As for
879:Support
840:Support
823:Support
241:before.
150:on the
41:C-class
847:bd2412
809:Mark M
795:– Per
186:merged
47:scale.
1021:Merge
289:, Ad(
188:into
1094:talk
1073:talk
1044:talk
1029:talk
1011:talk
995:talk
991:Taku
966:talk
941:talk
887:talk
883:Taku
868:talk
831:talk
813:talk
807:.
779:talk
491:of Ψ
474:talk
222:Tip:
142:High
989:--
902:.
881:--
450:is
1108::
1096:)
1075:)
1046:)
1031:)
1013:)
997:)
968:)
943:)
889:)
870:)
833:)
815:)
791:→
781:)
773:.
754:.
702:∂
682:Ψ
678:∂
628:∂
608:Ψ
604:∂
554:∂
543:Ψ
539:∂
476:)
433:−
385:
382:Ad
338:−
1092:(
1071:(
1042:(
1027:(
1009:(
993:(
964:(
939:(
885:(
866:(
854:T
829:(
811:(
777:(
722:e
719:=
716:h
711:|
705:h
697:)
694:h
691:(
686:g
648:e
645:=
642:g
637:|
631:g
623:)
620:h
617:(
612:g
574:e
571:=
568:g
563:|
557:g
547:g
507:g
494:g
472:(
463:g
459:g
452:S
436:1
429:g
425:S
422:g
398:s
394:)
391:g
388:(
379:=
375:′
371:s
341:1
334:g
330:S
327:g
324:=
320:′
317:S
303:S
299:g
295:s
291:g
287:g
202:.
154:.
53::
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
