The homology of \(\text{SL}_ 2(F[t,t^{-1}])\)
type: Item
instance of: scholarly article
title: The homology of \(\text{SL}_ 2(F[t,t^{-1}])\)
zbMATH Open document ID: 0846.20045
author: Kevin P. Knudson
published in: Journal of Algebra
publication date: 1996-06-03T00:00:00Z
review text: Let \(F\) be a number field. The author shows that \(H_k (SL_2 (F[t,t^{-1}]); \mathbb{Q}) \cong H_{k-1} (F^*; \mathbb{Q})\) provided that \(k \geq 2r + 3s + 2\), where \(r\) is the number of real embeddings, \(s\) the number of pairs of complex embeddings. The problem is broken up into manageable pieces by means of the action of \(SL_2(F[t, t^{-1}])\) on a tree and the associated spectral sequence. One of the intermediate results is that for an infinite field of characteristic zero \(H_k (SL_2 (F[t]); \mathbb{Q}) \cong H_k (SL_2(F); \mathbb{Q})\).
Mathematics Subject Classification ID: 20G10
Mathematics Subject Classification ID: 20G30
zbMATH DE Number: 869801
zbMATH Keywords: number fields
zbMATH Keywords: real embeddings
zbMATH Keywords: complex embeddings
zbMATH Keywords: actions
zbMATH Keywords: spectral sequences
reviewed by: Wilberd van der Kallen
MaRDI profile type: Publication
full work available at URL: jabr.1996.0053
OpenAlex ID: W2018455903
DOI: 10.1006/JABR.1996.0053
description: scientific article; zbMATH DE number 869801