Vol. 3, No. 4, 2009

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Equivariant Hilbert series

Frank Himstedt and Peter Symonds

Vol. 3 (2009), No. 4, 423–443
Abstract

We consider a finite group acting on a graded module and define an equivariant degree that generalizes the usual nonequivariant degree. The value of this degree is a module for the group, up to a rational multiple. We investigate how this behaves when the module is a ring and apply our results to reprove some results of Kuhn on the cohomology of groups.

Keywords
Hilbert series, group action, ring, degree, equivariant
Mathematical Subject Classification 2000
Primary: 13D40
Secondary: 20C20
Milestones
Received: 29 May 2008
Revised: 4 March 2009
Accepted: 18 March 2009
Published: 15 June 2009
Authors
Frank Himstedt
Technische Universität München
Zentrum Mathematik – M11
Boltzmannstr. 3
85748 Garching
Germany
Peter Symonds
School of Mathematics
University of Manchester
Manchester M13 9PL
United Kingdom