Congruence subgroups and twisted cohomology of SL_n(F[t])
| dc.creator | Knudson, Kevin P. | |
| dc.date | 1998-01-21 | |
| dc.date.accessioned | 2026-07-07T05:23:39Z | |
| dc.date.available | 2026-07-07T05:23:39Z | |
| dc.description | Let F be a field of characteristic zero and let V be an irreducible representation of SL_n(F). In this paper, we compute the first cohomology of SL_n(F[t]) with coefficients in V. It agrees with H^1(SL_n(F),V) if V is not the adjoint representation, while if V = Ad, the two groups differ by an F-vector space X. We show that if n=2, X is infinite dimensional, while if n>2, dim X = 1. We also study the abelianization of the kernel of the map SL_n(F[t])-->SL_n(F) given by setting t=0, where now F is any field. We conjecture that this abelianization is the adjoint representation sl_n(F) if n>2 and F is finite, and prove this in the case n=3, F=F_2, F_3. | |
| dc.description | 24 pages, 1 figure, to appear in Journal of Algebra | |
| dc.identifier | https://arxiv.org/abs/math/9801099 | |
| dc.identifier | http://arxiv.org/abs/math/9801099 | |
| dc.identifier | J. Algebra <b>207</b> (1998), 695-721 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76522 | |
| dc.subject | K-Theory and Homology | |
| dc.subject | Group Theory | |
| dc.subject | 20G10 | |
| dc.title | Congruence subgroups and twisted cohomology of SL_n(F[t]) | |
| dc.type | text |