Modular representations of profinite groups

MacQuarrie, J.W. (2009) Modular representations of profinite groups. [MIMS Preprint]

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Abstract

Our aim is to transfer several foundational results from the modular representation theory of finite groups to the wider context of profinite groups. We are thus interested in profinite modules over the completed group algebra of a profinite group, where the underlying field is a finite field of characteristic p. We define the concept of relative projectivity for such a module. We prove a characterization of finitely generated relatively projective modules analogous to the finite case with additions of interest to the profinite theory. We introduce vertices and sources for indecomposable finitely generated modules over the completed group algebra and show that the expected conjugacy properties hold - for sources this requires additional assumptions. Finally we prove a direct analogue of Green's Indecomposability Theorem for finitely generated modules over a virtually pro-p group

Item Type:	MIMS Preprint
Uncontrolled Keywords:	modular representation theory, profinite group, virtually pro-p group, relative projectivity, vertex, source, Green's indecomposability theorem, coinvariant
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 16 Associative rings and algebras MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations MSC 2010, the AMS's Mathematics Subject Classification > 22 Topological groups, Lie groups
Depositing User:	Dr J.W. MacQuarrie
Date Deposited:	03 May 2009
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1262

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