707:
167:
458:
231:
372:
513:
337:
299:
255:
90:
45:
552:
748:
98:
661:
Volodin, I. (1971), "Algebraic K-theory as extraordinary homology theory on the category of associative rings with unity",
782:
392:
175:
345:
767:
741:
482:
340:
772:
787:
777:
734:
312:
265:
240:
60:
690:
670:
621:
262:
8:
674:
722:
609:
461:
258:
48:
30:
387:
307:
234:
55:
682:
678:
650:
601:
686:
629:
617:
540:
237:
with 1's on the diagonal (i.e., the unipotent radical of the standard Borel) and
718:
654:
761:
303:
477:
17:
613:
605:
714:
21:
694:, (Translation: Math. USSR Izvestija Vol. 5 (1971) No. 4, 859–887)
706:
162:{\displaystyle X=\bigcup _{n,\sigma }B(U_{n}(R)^{\sigma })}
551:). This theorem was a pioneering result in the area of
302:
and acting (superscript) by conjugation. The space is
485:
395:
348:
315:
268:
243:
178:
101:
63:
33:
630:"The K-book: an introduction to algebraic K-theory"
588:Goodwillie, Thomas G. (1986), "Relative algebraic
507:
452:
366:
331:
293:
249:
225:
161:
84:
39:
759:
742:
637:Suslin, A. A. (1981), "On the equivalence of
749:
735:
587:
516:
453:{\displaystyle BGL(R)/X\simeq BGL^{+}(R)}
226:{\displaystyle U_{n}(R)\subset GL_{n}(R)}
472:An analogue of Volodin's space where GL(
660:
760:
636:
627:
571:
379:
367:{\displaystyle \operatorname {St} (R)}
701:
519:to prove that, after tensoring with
508:{\displaystyle {\mathfrak {gl}}(R)}
491:
488:
13:
14:
799:
705:
683:10.1070/IM1971v005n04ABEH001121
592:-theory and cyclic homology",
565:
502:
496:
467:
447:
441:
411:
405:
361:
355:
288:
282:
220:
214:
195:
189:
156:
147:
140:
127:
79:
73:
1:
581:
721:. You can help Knowledge by
539:, is isomorphic to relative
261:thought of as an element in
7:
388:Quillen's plus-construction
10:
804:
700:
655:10.1080/00927878108822666
535:), for a nilpotent ideal
332:{\displaystyle \pi _{1}X}
294:{\displaystyle GL_{n}(R)}
233:is the subgroup of upper
628:Weibel, Charles (2013).
574:, Ch. IV. Example 1.3.2.
558:
250:{\displaystyle \sigma }
20:, more specifically in
783:Representable functors
509:
454:
368:
333:
295:
251:
227:
163:
86:
85:{\displaystyle BGL(R)}
41:
594:Annals of Mathematics
510:
476:) is replaced by the
455:
369:
334:
296:
252:
228:
164:
87:
54:is a subspace of the
42:
663:Izv. Akad. Nauk SSSR
483:
393:
346:
313:
266:
241:
176:
99:
61:
31:
675:1971IzMat...5..859V
386:yields a model for
235:triangular matrices
768:Algebraic topology
505:
462:algebraic K-theory
450:
364:
329:
291:
259:permutation matrix
247:
223:
159:
123:
82:
37:
730:
729:
596:, Second Series,
517:Goodwillie (1986)
308:fundamental group
108:
56:classifying space
40:{\displaystyle X}
795:
751:
744:
737:
715:topology-related
709:
702:
693:
657:
633:
624:
575:
569:
514:
512:
511:
506:
495:
494:
459:
457:
456:
451:
440:
439:
418:
373:
371:
370:
365:
338:
336:
335:
330:
325:
324:
300:
298:
297:
292:
281:
280:
256:
254:
253:
248:
232:
230:
229:
224:
213:
212:
188:
187:
168:
166:
165:
160:
155:
154:
139:
138:
122:
91:
89:
88:
83:
46:
44:
43:
38:
803:
802:
798:
797:
796:
794:
793:
792:
773:Homotopy theory
758:
757:
756:
755:
698:
649:(15): 1559–66,
606:10.2307/1971283
584:
579:
578:
570:
566:
561:
541:cyclic homology
487:
486:
484:
481:
480:
470:
435:
431:
414:
394:
391:
390:
347:
344:
343:
341:Steinberg group
320:
316:
314:
311:
310:
276:
272:
267:
264:
263:
242:
239:
238:
208:
204:
183:
179:
177:
174:
173:
150:
146:
134:
130:
112:
100:
97:
96:
62:
59:
58:
32:
29:
28:
12:
11:
5:
801:
791:
790:
788:Topology stubs
785:
780:
775:
770:
754:
753:
746:
739:
731:
728:
727:
710:
696:
695:
669:(4): 844–873,
658:
634:
625:
600:(2): 347–402,
583:
580:
577:
576:
563:
562:
560:
557:
504:
501:
498:
493:
490:
469:
466:
449:
446:
443:
438:
434:
430:
427:
424:
421:
417:
413:
410:
407:
404:
401:
398:
363:
360:
357:
354:
351:
328:
323:
319:
290:
287:
284:
279:
275:
271:
246:
222:
219:
216:
211:
207:
203:
200:
197:
194:
191:
186:
182:
170:
169:
158:
153:
149:
145:
142:
137:
133:
129:
126:
121:
118:
115:
111:
107:
104:
81:
78:
75:
72:
69:
66:
36:
9:
6:
4:
3:
2:
800:
789:
786:
784:
781:
779:
778:Fiber bundles
776:
774:
771:
769:
766:
765:
763:
752:
747:
745:
740:
738:
733:
732:
726:
724:
720:
717:article is a
716:
711:
708:
704:
703:
699:
692:
688:
684:
680:
676:
672:
668:
664:
659:
656:
652:
648:
644:
643:Comm. Algebra
640:
635:
631:
626:
623:
619:
615:
611:
607:
603:
599:
595:
591:
586:
585:
573:
568:
564:
556:
554:
553:trace methods
550:
546:
542:
538:
534:
530:
526:
522:
518:
499:
479:
475:
465:
463:
444:
436:
432:
428:
425:
422:
419:
415:
408:
402:
399:
396:
389:
385:
381:
380:Suslin (1981)
377:
358:
352:
349:
342:
326:
321:
317:
309:
305:
301:
285:
277:
273:
269:
260:
244:
236:
217:
209:
205:
201:
198:
192:
184:
180:
151:
143:
135:
131:
124:
119:
116:
113:
109:
105:
102:
95:
94:
93:
76:
70:
67:
64:
57:
53:
50:
34:
27:
26:Volodin space
23:
19:
723:expanding it
712:
697:
666:
662:
646:
642:
641:-theories",
638:
597:
593:
589:
567:
548:
544:
536:
532:
528:
524:
520:
515:was used by
473:
471:
383:
382:showed that
375:
171:
51:
25:
15:
572:Weibel 2013
523:, relative
478:Lie algebra
468:Application
378:. In fact,
18:mathematics
762:Categories
582:References
527:-theory K(
423:≃
353:
318:π
245:σ
199:⊂
152:σ
120:σ
110:⋃
92:given by
306:and the
22:topology
691:0296140
671:Bibcode
622:0855300
614:1971283
339:is the
304:acyclic
689:
620:
612:
172:where
24:, the
713:This
610:JSTOR
559:Notes
47:of a
719:stub
49:ring
679:doi
651:doi
602:doi
598:124
543:HC(
460:in
374:of
16:In
764::
687:MR
685:,
677:,
667:35
665:,
645:,
618:MR
616:,
608:,
555:.
547:,
531:,
464:.
350:St
257:a
750:e
743:t
736:v
725:.
681::
673::
653::
647:9
639:K
632:.
604::
590:K
549:I
545:A
537:I
533:I
529:A
525:K
521:Q
503:)
500:R
497:(
492:l
489:g
474:R
448:)
445:R
442:(
437:+
433:L
429:G
426:B
420:X
416:/
412:)
409:R
406:(
403:L
400:G
397:B
384:X
376:R
362:)
359:R
356:(
327:X
322:1
289:)
286:R
283:(
278:n
274:L
270:G
221:)
218:R
215:(
210:n
206:L
202:G
196:)
193:R
190:(
185:n
181:U
157:)
148:)
144:R
141:(
136:n
132:U
128:(
125:B
117:,
114:n
106:=
103:X
80:)
77:R
74:(
71:L
68:G
65:B
52:R
35:X
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
