Extension groups between simple Mackey functors
type: Item
instance of: scholarly article
title: Extension groups between simple Mackey functors
zbMATH Open document ID: 1163.19001
author: Muriel Nicollerat
published in: Journal of Algebra
publication date: 2009-04-21T00:00:00Z
review text: A Mackey functor for a finite group \(G\) over an algebraically closed field \(k\) of characteristic \(p>0\) can be viewed as a module over the Mackey algebra \(\mu_k(G)\). For every subgroup \(H\) of \(G\) and every simple \(kN_G(H)/H\)-module \(V\), there is a simple Mackey funktor \(S_{H,V}\) for \(G\) over \(k\). In the paper under review, the author investigates the groups \(\text{Ext}^1_{\mu_k(G)}(S_{Q,W}, S_{H,V})\), for subgroups \(Q,H\) of \(G\), a simple \(kN_G(H)/H\)-module \(V\) and a simple \(kN_G(Q)/Q\)-module \(W\). One of her main results is concerned with the case where \(Q\) and \(H\) are distinct normal subgroups of \(G\). Another deals with the case where \(Q\) and \(H\) are non-conjugate, and \(V,W\) are both trivial. A third result handles the case where \(G\) has a normal Sylow \(p\)-subgroup and \(Q,H\) are non-conjugate. Finally, the author relates \(\text{Ext}^1_{\mu_k(G)}(S_{H,V}, S_{H,W})\) and \(\text{Ext}^1_{N_G(H)/H}(V,W)\) when either \(V,W\) are both trivial, or \(G\) has a normal Sylow \(p\)-subgroup.
reviewed by: Burkhard Külshammer
Mathematics Subject Classification ID: 19A22
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 18G15
zbMATH DE Number: 5545851
zbMATH Keywords: Mackey functor
zbMATH Keywords: Mackey algebra
zbMATH Keywords: extension group
zbMATH Keywords: group representation
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2008.11.002
OpenAlex ID: W2061793303
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DOI: 10.1016/J.JALGEBRA.2008.11.002
description: scientific article; zbMATH DE number 5545851