A variant of the Reynolds operators

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Title:	A variant of the Reynolds operators
Authors:	Chu, Huah;胡守仁;Hu, Shou-jen;Kang, Ming-chang
Contributors:	淡江大學數學學系
Date:	2005-10
Issue Date:	2010-01-28 07:12:26 (UTC+8)
Publisher:	Providence: American Mathematical Society (AMS)
Abstract:	Let G be a linearly reductive group over a field k, and let R be a kalgebra with a rational action of G. Given rational R-G-modules M and N, we define for the induced G-action on HomR(M,N) a generalized Reynolds operator, which exists even if the action on HomR(M,N) is not rational. Given an R-module homomorphism M → N, it produces, in a naturalway, an R-module homomorphism which is G-equivariant. We use this generalized Reynolds operator to study properties of rational R-G modules. In particular, we prove that if M is invariantly generated (i.e. M = R·MG), then MG is a projective (resp. flat) RG-module provided that M is a projective (resp. flat) R-module. We also give a criterion whether an R-projective (or R-flat) rational R-G-module is extended from an RG-module.
Relation:	Proceedings of the American Mathematical Society 133(10), pp.2865-2871
DOI:	10.1090/S0002-9939-05-07845-7
Appears in Collections:	[Graduate Institute & Department of Mathematics] Journal Article

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