Campbell, Eddy and GeramitaI, A.V. and Hughes, I.P. and Wehlau, David L. and Shank, R. James (1999) NonCohenMacaulay Vector Invariants and a Noether Bound for a Gorenstein Ring of Invariants. Canadian Mathematical BulletinBulletin Canadien De Mathematiques, 42 (2). pp. 155161. ISSN 00084395. (Full text available)
PDF  Published Version  
Download (64kB)
Preview


Abstract
This paper contains two essentially independent results in the invariant theory of finite groups. First we prove that, for any faithful representation of a nontrivial pgroup over a field of characteristic p, the ring of vector invariants ofmcopies of that representation is not CohenMacaulay 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 nontrivial 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 > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Pure Mathematics 
Depositing User:  R James Shank 
Date Deposited:  13 Jun 2009 13:24 
Last Modified:  18 Jun 2014 13:53 
Resource URI:  https://kar.kent.ac.uk/id/eprint/4643 (The current URI for this page, for reference purposes) 
 Export to:
 RefWorks
 EPrints3 XML
 CSV
 Depositors only (login required):
Downloads
Downloads per month over past year