The Cohen-Macaulay property of separating invariants of finite groups

Dufresne, Emilie and Elmer, Jonathan and Kohls, Martin (2009) The Cohen-Macaulay property of separating invariants of finite groups. Transformation Groups, 14 (4). pp. 771-785. ISSN 1083-4362

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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 sep-
arating algebra is Cohen-Macaulay. Furthermore, we show that,
for a p-group, the existence of a Cohen-Macaulay graded separat-
ing algebra implies the group is generated by bireflections. Ad-
ditionally, we give an example which shows that Cohen-Macaulay
separating algebras can occur when the ring of invariants is not
Cohen-Macaulay.

Item Type: Article
Research Areas: A. > School of Science and Technology > Design Engineering and Mathematics
Item ID: 19306
Depositing User: Jonathan Elmer
Date Deposited: 15 Apr 2016 09:38
Last Modified: 09 Nov 2018 01:51
URI: http://eprints.mdx.ac.uk/id/eprint/19306

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