Invariant rings of orthogonal groups over F-2

Kropholler, P.H., Rajaei, S.M. and Segal, J. (2005) Invariant rings of orthogonal groups over F-2. Glasgow Mathematical Journal, 47(1), pp. 7-54. (doi: 10.1017/S0017089504002198)

Abstract

We determine the rings of invariants SG where S is the symmetric algebra on the dual of a vector space V over 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 dimV, and it is shown to be a complete intersection. In particular, the rings of invariants computed here are all Gorenstein and hence Cohen-Macaulay.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Kropholler, Prof Peter
• Authors: Kropholler, P.H., Rajaei, S.M., and Segal, J.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Glasgow Mathematical Journal
• Publisher: Cambridge University Press
• ISSN: 0017-0895
• ISSN (Online): 1469-509X
• Published Online: 31 January 2005
• Copyright Holders: Copyright © 2005 Glasgow Mathematical Journal Trust
• First Published: First published in Glasgow Mathematical Journal 47(1):7-54
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher