Mathematical Research Letters

Volume 21 (2014)

Number 6

On homology of linear groups over $k[\mathrm{t}]$

Pages: 1483 – 1500

DOI: http://dx.doi.org/10.4310/MRL.2014.v21.n6.a15

Author

Matthias Wendt (Fakultät Mathematik, Universität Duisburg, Essen, Germany)

Abstract

This note explains how to prove that for any simply-connected reductive group $G$ and any infinite field $k$, the inclusion $k \hookrightarrow k[\mathrm{t}]$ induces an isomorphism on group homology. This generalizes results of Soulé and Knudson.

Keywords

linear groups, polynomial rings, group homology, homotopy invariance

2010 Mathematics Subject Classification

20E42, 20G10

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