Non-Cohen-Macaulay Vector Invariants and a Noether Bound for a Gorenstein Ring of Invariants

Campbell, Eddy and GeramitaI, A.V. and Hughes, I.P. and Wehlau, David L. and Shank, R. James (1999) Non-Cohen-Macaulay Vector Invariants and a Noether Bound for a Gorenstein Ring of Invariants. Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques, 42 (2). pp. 155-161. ISSN 0008-4395. (Full text available)

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This paper contains two essentially independent results in the invariant theory of finite groups. First we prove that, for any faithful representation of a non-trivial p-group over a field of characteristic p, the ring of vector invariants ofmcopies of that representation is not Cohen-Macaulay form 3. In the second section of the paper we use Poincar´e series methods to produce upper bounds for the degrees of the generators for the ring of invariants as long as that ring is Gorenstein. We prove that, for a finite non-trivial group G and a faithful representation of dimension n with n > 1, if the ring of invariants is Gorenstein then the ring is generated in degrees less than or equal to n(jGj − 1). If the ring of invariants is a hypersurface, the upper bound can be improved to [G].

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science) > QA150 Algebra
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: R James Shank
Date Deposited: 13 Jun 2009 13:24 UTC
Last Modified: 18 Jun 2014 13:53 UTC
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