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# Invariant rings of orthogonal groups over ${\mathbb F}_2$

Kropholler, P.H., Mohseni Rajaei, S. and Segal, J. (2005) Invariant rings of orthogonal groups over ${\mathbb F}_2$. Glasgow Mathematical Journal, 47 (1), 7-54.

Record type: Article

## Abstract

We determine the rings of invariants $S^G$ where $S$ is the symmetric algebra on the dual of a vector space $V$ over ${\mathbb F}_2$ and $G$ is the orthogonal group preserving a non-singular quadratic form on $V$. The invariant ring is shown to have a presentation in which the difference between the number of generators and the number of relations is equal to the minimum possibility, namely $\dim V$, and it is shown to be a complete intersection. In particular, the rings of invariants computed here are all Gorenstein and hence Cohen-Macaulay

Published date: 31 January 2005
Organisations: Mathematical Sciences

## Identifiers

Local EPrints ID: 349591
URI: http://eprints.soton.ac.uk/id/eprint/349591
ISSN: 0017-0895
PURE UUID: d586536e-e2e4-460d-9782-7be8da3b93b3
ORCID for P.H. Kropholler: orcid.org/0000-0001-5460-1512

## Catalogue record

Date deposited: 11 Mar 2013 14:19

## Contributors

Author: P.H. Kropholler
Author: S. Mohseni Rajaei
Author: J. Segal