The Lenstra map on classifying spaces and G-theory of group rings
type: Item
instance of: scholarly article
title: The Lenstra map on classifying spaces and G-theory of group rings
zbMATH Open document ID: 0589.55008
DOI: 10.1007/BF01388733
published in: Inventiones Mathematicae
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143334
review text: Let G be a finite group, R a Noetherian ring, and \(G_*(RG)\) the Quillen K-theory of the category of finitely generated RG-modules, where RG is the group ring of G with coefficients in R. H. Lenstra has derived an ingenious formula for \(G_ 0(RG)\) when G is abelian, and the author generalized Lenstra's work to compute \(G_ n(RG)\), \(n\geq 1\), for abelian G and many R (including \(R={\mathbb{Z}})\). In this paper the author lifts Lenstra's construction to a functor on the level of classifying spaces which is a homotopy equivalence. This allows him to improve his earlier results by including more general coefficient rings R and some non- abelian groups G (for example, dihedral groups).
Mathematics Subject Classification ID: 55R35
Mathematics Subject Classification ID: 18F25
Mathematics Subject Classification ID: 16E20
zbMATH DE Number: 3947211
zbMATH Keywords: abelian groups
zbMATH Keywords: finite group
zbMATH Keywords: Quillen K-theory
zbMATH Keywords: classifying spaces
zbMATH Keywords: dihedral groups
author: David L. Webb
reviewed by: Michael R. Stein
MaRDI profile type: Publication
cites work: Q5518494
cites work: Grothendieck groups of integral group rings
cites work: The group \(K_3(Z)\) is cyclic of order forty-eight
cites work: Grothendieck groups of Abelian group rings
cites work: Higher algebraic K-theory: I
cites work: Grothendieck groups of dihedral and quaternion group rings
cites work: Quillen G-theory of Abelian group rings
cites work: Q5723265
OpenAlex ID: W1983936732
description: scientific article; zbMATH DE number 3947211