Homology of \(Gl(R)\) with coefficients in a functor of finite degree
type: Item
instance of: scholarly article
title: Homology of \(Gl(R)\) with coefficients in a functor of finite degree
zbMATH Open document ID: 0808.20042
DOI: 10.1016/S0021-8693(05)80050-X
author: Stanislaw Betley
published in: Journal of Algebra
publication date: 1992-09-27T00:00:00Z
review text: In the present note we study the homology groups of \(Gl_ n R\) with twisted coefficients for \(R\) a commutative ring with unit. Let \(i_ n\) be the group homomorphism from \(Gl_ n R\) to \(Gl_{n + 1} R\) which sends \(X\) to \(\left | \begin{smallmatrix} X\;0\\0\;I \end{smallmatrix} \right |\). Moreover, assume that for every \(n\) we have a \(Gl_ n R\)-module \(M_ n\) and a \(Gl_ n R\)-homomorphism \(F_ n : M_ n \to M_{n + 1}\). The set \(\{M_ n\}\) will be called a coefficient system for \(Gl_ n R\). Let \(Gl R\) denote \(\lim_{n \to \infty} Gl_ n R\) and \(M = \lim_{n \to \infty} M_ n\). We are especially interested in finding \(H_ * (Gl R;M)\).
Mathematics Subject Classification ID: 20G10
Mathematics Subject Classification ID: 20G35
Mathematics Subject Classification ID: 55N25
Mathematics Subject Classification ID: 19D55
zbMATH DE Number: 63895
zbMATH Keywords: homology groups
zbMATH Keywords: twisted coefficients
zbMATH Keywords: commutative ring
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 63895