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

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

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

7-54

Kropholler, P.H.

0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4

Mohseni Rajaei, S.

1340064d-4862-4b73-8b05-32218777aa0e

Segal, J.

14ced8bf-2de3-41d3-a854-da55379a9f9f

31 January 2005

Kropholler, P.H.

0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4

Mohseni Rajaei, S.

1340064d-4862-4b73-8b05-32218777aa0e

Segal, J.

14ced8bf-2de3-41d3-a854-da55379a9f9f

Kropholler, P.H., Mohseni Rajaei, S. and Segal, J.
(2005)
Invariant rings of orthogonal groups over ${\mathbb F}_2$.
*Glasgow Mathematical Journal*, 47 (1), .
(doi:10.1017/S0017089504002198).

## 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

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## More information

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

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Date deposited: 11 Mar 2013 14:19

Last modified: 03 Dec 2019 01:37

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## Contributors

Author:
S. Mohseni Rajaei

Author:
J. Segal

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