Some remarks on projective Mackey functors
type: Item
instance of: scholarly article
title: Some remarks on projective Mackey functors
zbMATH Open document ID: 0757.19001
DOI: 10.1016/0022-4049(92)90132-Y
published in: Journal of Pure and Applied Algebra
publication date: 1992-09-27T00:00:00Z
review text: This paper discusses Mackey functors on a finite group \(G\). Among the results are the following: a Mackey functor has projective dimension 0, 1 or \(\infty\); the Grothendieck \(G\)-theory of Mackey functors is computable in terms of the \(G\)-theories of Weyl groups; the same applies to \(K\)- theory for Mackey functors whose values are modules over a ring in which the order of \(G\) is invertible. The author also computes the projective class groups of Mackey functors for groups of prime order and gives applications to equivariant stable homotopy theory. In particular, there is no stable \(G\)-Moore spectrum for the integers if \(G\) is a non-trivial.
Mathematics Subject Classification ID: 19A22
Mathematics Subject Classification ID: 20J05
Mathematics Subject Classification ID: 55P91
zbMATH DE Number: 64209
zbMATH Keywords: Burnside functor
zbMATH Keywords: Mackey functors on a finite group
zbMATH Keywords: projective dimension
zbMATH Keywords: Grothendieck \(G\)-theory
zbMATH Keywords: \(G\)-theories of Weyl groups
zbMATH Keywords: \(K\)- theory
zbMATH Keywords: projective class groups
zbMATH Keywords: equivariant stable homotopy theory
zbMATH Keywords: \(G\)- Moore spectrum
author: John Greenlees
reviewed by: Richard John Steiner
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 64209