Fleischmann, P. and Woodcock, C.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.
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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).
|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:||28 Nov 2012 10:02|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/28565 (The current URI for this page, for reference purposes)|
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