On the depth of separating algebras for finite groups

Jonathan Elmer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Consider a finite group G acting on a vector space V over a field K of characteristic p > 0. A separating algebra is a subalgebra A of the ring of invariants K[V] G with the same point separation properties. In this article we compare the depth of an arbitrary separating algebra with that of the corresponding ring of invariants. We show that, in some special cases, the depth of A is bounded above by the depth of K[V] G.

Original languageEnglish
Pages (from-to)31-39
Number of pages9
JournalBeiträge zur Algebra und Geometrie
Issue number1
Early online date11 May 2011
Publication statusPublished - Mar 2012

Bibliographical note

This work was completed during a short stay at RWTH-Aachen. The author would
like to thank Julia Hartmann for making this stay possible. Special thanks go to Martin Kohls for Example 5.1 and various useful MAGMA routines, and to an anonymous referee for a couple of helpful suggestions.


  • Cohomology modules
  • Depth
  • Invariant theory
  • Modular representation theory
  • Separating algebra


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