Third homology of general linear groups
| dc.creator | Mirzaii, Behrooz | |
| dc.date | 2003-12-22 | |
| dc.date | 2007-10-20 | |
| dc.date.accessioned | 2026-07-07T08:37:10Z | |
| dc.date.available | 2026-07-07T08:37:10Z | |
| dc.description | The third homology group of GL_n(R) is studied, where R is a `ring with many units' with center Z(R). The main theorem states that if K_1(Z(R))_Q \simeq K_1(R)_Q, (e.g. R a commutative ring or a central simple algebra), then H_3(GL_2(R), Q) --> H_3(GL_3(R), Q) is injective. If R is commutative, Q can be replaced by a field k such that 1/2 is in k. For an infinite field R (resp. an infinite field R such that R*=R*^2), we get a better result that H_3(GL_2(R), Z[1/2] --> H_3(GL_3(R), Z[1/2]) (resp. H_3(GL_2(R), Z) --> H_3(GL_3(R), Z)) is injective. As an application we study the third homology group of SL_2(R) and the indecomposable part of K_3(R). | |
| dc.description | 24 pages, Latex, new title, some results are generalized, added references | |
| dc.identifier | https://arxiv.org/abs/math/0312409 | |
| dc.identifier | http://arxiv.org/abs/math/0312409 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140308 | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 19D55;19D45 | |
| dc.title | Third homology of general linear groups | |
| dc.type | text |