On the coinvariants of modular representations of cyclic groups of prime order

Sezer, Müfit and Shank, R. James (2006) On the coinvariants of modular representations of cyclic groups of prime order. Journal of Pure and Applied Algebra, 205 (1). pp. 210-225. ISSN 0022-4049. (doi:https://doi.org/10.1016/j.jpaa.2005.07.003 ) (Full text available)

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Official URL http://dx.doi.org/doi:10.1016/j.jpaa.2005.07.003

Abstract

We consider the ring of coinvariants for modular representations of cyclic groups of prime order. For all cases for which explicit generators for the ring of invariants are known, we give a reduced Gröbner basis for the Hilbert ideal and the corresponding monomial basis for the coinvariants. We also describe the decomposition of the coinvariants as a module over the group ring. For one family of representations, we are able to describe the coinvariants despite the fact that an explicit generating set for the invariants is not known. In all cases our results confirm the conjecture of Harm Derksen and Gregor Kemper on degree bounds for generators of the Hilbert ideal. As an incidental result, we identify the coefficients of the monomials appearing in the orbit product of a terminal variable for the three-dimensional indecomposable representation.

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:	09 May 2008 10:46 UTC
Last Modified:	26 Jun 2017 18:35 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/3117 (The current URI for this page, for reference purposes)