The Cohen-Macaulay property of separating invariants of finite groups

Emilie Dufresne*, Jonathan Elmer, Martin Kohls

*Corresponding author for this work

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

In the case of finite groups, a separating algebra is a subalgebra of the ring of invariants which separates the orbits. Although separating algebras are often better behaved than the ring of invariants, we show that many of the criteria which imply the ring of invariants is non-Cohen-Macaulay actually imply that no graded separating algebra is Cohen-Macaulay. For example, we show that, over a field of positive characteristic p, given sufficiently many copies of a faithful modular representation, no graded separating algebra is Cohen-Macaulay. Furthermore, we show that, for a p-group, the existence of a Cohen-Macaulay graded separating algebra implies the group is generated by bireections. Additionally, we give an example which shows that Cohen-Macaulay separating algebras can occur when the ring of invariants is not Cohen-Macaulay.

Original languageEnglish
Pages (from-to)771-785
Number of pages15
JournalTransformation Groups
Volume14
Issue number4
Early online date14 Nov 2009
DOIs
Publication statusPublished - Dec 2009

Keywords

  • COMPUTING INVARIANTS
  • REDUCTIVE GROUPS
  • RINGS

Cite this