Relative Invariants, Ideal Classes and Quasi-Canonical Modules of Modular Rings of Invariants

Fleischmann, Peter and Woodcock, Chris F. (2011) Relative Invariants, Ideal Classes and Quasi-Canonical Modules of Modular Rings of Invariants. Journal of Algebra, 348 (1). pp. 110-134. ISSN 0021-8693. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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Official URL
http://dx.doi.org/10.1016/j.jalgebra.2011.09.024

Abstract

We describe “quasi-canonical modules” for modular invariant rings R of finite group actions on factorial Gorenstein domains. From this we derive a general “quasi-Gorenstein criterion” in terms of certain 1-cocycles. This generalizes a recent result of A. Braun for linear group actions on polynomial rings, which itself generalizes a classical result of Watanabe for non-modular invariant rings. We use an explicit classification of all reflexive rank one R-modules, which is given in terms of the class group of R, or in terms of R-semi-invariants. This result is implicitly contained in a paper of Nakajima (1982).

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: Chris F Woodcock
Date Deposited: 02 Jan 2012 01:02
Last Modified: 19 May 2014 13:26
Resource URI: https://kar.kent.ac.uk/id/eprint/28565 (The current URI for this page, for reference purposes)
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