Equivariant Hilbert series

Himstedt, Frank; Symonds, Peter

doi:10.2140/ant.2009.3.423

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Equivariant Hilbert series

Frank Himstedt and Peter Symonds

Vol. 3 (2009), No. 4, 423–443

DOI: 10.2140/ant.2009.3.423

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

Vol. 3, No. 4, 2009