84:
74:
53:
22:
793:
I agree the statement can use a clarification on the meaning of automorphism group. (I know I am the one who added the statement but I have no idea what I meant.) By the real case, I think it refers to the diffeomorphism group, but thatβs generally an infinite-dimensional Lie group. β-
610:
640:
385:
401:
140:
776:
701:
302:
739:
231:
197:
823:
130:
818:
106:
644:
389:
97:
58:
605:{\displaystyle (g_{1}g_{2}\cdot f)(h)=(g_{1}\cdot (g_{2}\cdot f))(h)=(g_{2}\cdot f)(g_{1}^{-1}h)=f(g_{2}^{-1}g_{1}^{-1}h)}
33:
749:
674:
244:
21:
799:
617:
39:
83:
633:
706:
105:
on
Knowledge. If you would like to participate, please visit the project page, where you can join
89:
639:
It would immeasurably improve this article if that table or a similar one were reproduced here.
73:
52:
795:
613:
210:
182:
812:
233:
spans a finite-dimensional vector space inside the ring of holomorphic functions on
782:", since it is unclear what *structure* is assumed to exist on the real maniifold.
636:, which contains a fairly short table of the most essential complex Lie groups.
102:
79:
803:
648:
621:
393:
612:. So it looks ok to me. Remember you unwind the outmost action first. --
179:
admits a natural structure of a linear algebraic group as follows:let
164:
Linear algebraic group associated to a complex semisimple Lie group
15:
671:
be a compact complex manifold. Then, as in the real case,
752:
709:
677:
404:
247:
213:
185:
101:, a collaborative effort to improve the coverage of
770:
733:
695:
604:
296:
225:
191:
8:
703:is a complex Lie group whose Lie algebra is
632:This article inludes a link to the article
336:But by the definition of a left action, (g
47:
19:
751:
708:
676:
587:
582:
569:
564:
536:
531:
509:
472:
456:
422:
412:
403:
279:
246:
212:
184:
175:be a complex semisimple Lie group. Then
771:{\displaystyle \operatorname {Aut} (X)}
696:{\displaystyle \operatorname {Aut} (X)}
384:, h in G, which is not generally true.
49:
297:{\displaystyle g\cdot f(h)=f(g^{-1}h)}
641:2601:200:C000:1A0:5DA5:7EC9:7DD6:DDD1
386:2601:200:C000:1A0:C820:3D3D:D3F2:D688
360:, h in G. But then we would have f((g
199:be the ring of holomorphic functions
7:
95:This article is within the scope of
38:It is of interest to the following
710:
14:
824:Low-priority mathematics articles
746:But it is not at all clear what "
115:Knowledge:WikiProject Mathematics
118:Template:WikiProject Mathematics
82:
72:
51:
20:
819:Stub-Class mathematics articles
135:This article has been rated as
765:
759:
728:
713:
690:
684:
628:How about more basic examples?
599:
557:
548:
524:
521:
502:
496:
490:
487:
484:
465:
449:
443:
437:
434:
405:
291:
272:
263:
257:
1:
734:{\displaystyle \Gamma (X,TX)}
654:Unclear statement in Examples
109:and see a list of open tasks.
840:
804:07:04, 17 March 2023 (UTC)
649:19:35, 3 August 2022 (UTC)
241:acts by left translation:
785:Hence nobody knows what "
134:
67:
46:
622:08:34, 24 May 2022 (UTC)
394:01:42, 24 May 2022 (UTC)
226:{\displaystyle G\cdot f}
141:project's priority scale
98:WikiProject Mathematics
772:
735:
697:
606:
298:
227:
193:
28:This article is rated
773:
736:
698:
607:
299:
228:
194:
750:
707:
675:
402:
245:
211:
183:
121:mathematics articles
662:includes this one:
634:Table of Lie groups
595:
577:
544:
166:begins as follows:
768:
731:
693:
602:
578:
560:
527:
294:
223:
189:
90:Mathematics portal
34:content assessment
192:{\displaystyle A}
155:
154:
151:
150:
147:
146:
831:
780:in the real case
777:
775:
774:
769:
740:
738:
737:
732:
702:
700:
699:
694:
611:
609:
608:
603:
594:
586:
576:
568:
543:
535:
514:
513:
477:
476:
461:
460:
427:
426:
417:
416:
352:β
f(h)) for all g
317:)β
f(h) = f((g
303:
301:
300:
295:
287:
286:
232:
230:
229:
224:
198:
196:
195:
190:
123:
122:
119:
116:
113:
92:
87:
86:
76:
69:
68:
63:
55:
48:
31:
25:
24:
16:
839:
838:
834:
833:
832:
830:
829:
828:
809:
808:
748:
747:
705:
704:
673:
672:
656:
630:
505:
468:
452:
418:
408:
400:
399:
383:
379:
375:
371:
367:
363:
359:
355:
351:
347:
343:
339:
332:
328:
324:
320:
316:
312:
275:
243:
242:
209:
208:
181:
180:
160:
120:
117:
114:
111:
110:
88:
81:
61:
32:on Knowledge's
29:
12:
11:
5:
837:
835:
827:
826:
821:
811:
810:
807:
806:
778:" would mean "
767:
764:
761:
758:
755:
730:
727:
724:
721:
718:
715:
712:
692:
689:
686:
683:
680:
655:
652:
629:
626:
625:
624:
601:
598:
593:
590:
585:
581:
575:
572:
567:
563:
559:
556:
553:
550:
547:
542:
539:
534:
530:
526:
523:
520:
517:
512:
508:
504:
501:
498:
495:
492:
489:
486:
483:
480:
475:
471:
467:
464:
459:
455:
451:
448:
445:
442:
439:
436:
433:
430:
425:
421:
415:
411:
407:
381:
377:
373:
369:
365:
361:
357:
353:
349:
345:
341:
337:
330:
326:
322:
318:
314:
310:
293:
290:
285:
282:
278:
274:
271:
268:
265:
262:
259:
256:
253:
250:
222:
219:
216:
188:
159:
158:Is this right?
156:
153:
152:
149:
148:
145:
144:
133:
127:
126:
124:
107:the discussion
94:
93:
77:
65:
64:
56:
44:
43:
37:
26:
13:
10:
9:
6:
4:
3:
2:
836:
825:
822:
820:
817:
816:
814:
805:
801:
797:
792:
791:
790:
788:
787:the real case
783:
781:
762:
756:
753:
744:
742:
725:
722:
719:
716:
687:
681:
678:
668:
663:
661:
653:
651:
650:
646:
642:
637:
635:
627:
623:
619:
615:
596:
591:
588:
583:
579:
573:
570:
565:
561:
554:
551:
545:
540:
537:
532:
528:
518:
515:
510:
506:
499:
493:
481:
478:
473:
469:
462:
457:
453:
446:
440:
431:
428:
423:
419:
413:
409:
398:
397:
396:
395:
391:
387:
376:h)) for all g
334:
307:
305:
288:
283:
280:
276:
269:
266:
260:
254:
251:
248:
238:
234:
220:
217:
214:
204:
200:
186:
176:
172:
167:
165:
157:
142:
138:
132:
129:
128:
125:
108:
104:
100:
99:
91:
85:
80:
78:
75:
71:
70:
66:
60:
57:
54:
50:
45:
41:
35:
27:
23:
18:
17:
786:
784:
779:
745:
670:
666:
664:
659:
658:The section
657:
638:
631:
344:)β
f(h) = (g
335:
308:
240:
236:
206:
202:
178:
174:
170:
168:
163:
162:The section
161:
137:Low-priority
136:
96:
62:Lowβpriority
40:WikiProjects
309:But then (g
112:Mathematics
103:mathematics
59:Mathematics
813:Categories
368:h)) = f((g
325:)h) = f((g
207:such that
30:Stub-class
789:" means.
660:Examples
139:on the
237:(here
36:scale.
348:)β
(g
333:h)).
800:talk
796:Taku
667:Let
645:talk
618:talk
614:Taku
390:talk
171:Let
754:Aut
679:Aut
380:, g
356:, g
203:on
131:Low
815::
802:)
757:β‘
743:"
711:Ξ
682:β‘
647:)
620:)
589:β
571:β
538:β
516:β
479:β
463:β
429:β
392:)
306:"
304:).
281:β
252:β
218:β
798:(
766:)
763:X
760:(
741:.
729:)
726:X
723:T
720:,
717:X
714:(
691:)
688:X
685:(
669:X
665:"
643:(
616:(
600:)
597:h
592:1
584:1
580:g
574:1
566:2
562:g
558:(
555:f
552:=
549:)
546:h
541:1
533:1
529:g
525:(
522:)
519:f
511:2
507:g
503:(
500:=
497:)
494:h
491:(
488:)
485:)
482:f
474:2
470:g
466:(
458:1
454:g
450:(
447:=
444:)
441:h
438:(
435:)
432:f
424:2
420:g
414:1
410:g
406:(
388:(
382:2
378:1
374:2
372:g
370:1
366:1
364:g
362:2
358:2
354:1
350:2
346:1
342:2
340:g
338:1
331:1
329:g
327:2
323:2
321:g
319:1
315:2
313:g
311:1
292:)
289:h
284:1
277:g
273:(
270:f
267:=
264:)
261:h
258:(
255:f
249:g
239:G
235:G
221:f
215:G
205:G
201:f
187:A
177:G
173:G
169:"
143:.
42::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
