A variant of the Reynolds operator

Authors:
Huah Chu, Shou-Jen Hu and Ming-chang Kang

Journal:
Proc. Amer. Math. Soc. **133** (2005), 2865-2871

MSC (2000):
Primary 13A50, 16D40, 16W22

Published electronically:
March 31, 2005

MathSciNet review:
2159763

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a linearly reductive group over a field , and let be a -algebra with a rational action of . Given rational --modules and , we define for the induced -action on Hom a generalized Reynolds operator, which exists even if the action on Hom is not rational. Given an -module homomorphism , it produces, in a natural way, an -module homomorphism which is -equivariant. We use this generalized Reynolds operator to study properties of rational - modules. In particular, we prove that if is invariantly generated (i.e. ), then is a projective (resp. flat) -module provided that is a projective (resp. flat) -module. We also give a criterion whether an -projective (or -flat) rational --module is extended from an -module.

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Additional Information

**Huah Chu**

Affiliation:
Department of Mathematics, National Taiwan University, Taipei, Taiwan

**Shou-Jen Hu**

Affiliation:
Department of Mathematics, Tamkang University, Taipei, Taiwan

**Ming-chang Kang**

Affiliation:
Department of Mathematics, National Taiwan University, Taipei, Taiwan

Email:
kang@math.ntu.edu.tw

DOI:
http://dx.doi.org/10.1090/S0002-9939-05-07845-7

Keywords:
Rings of invariants,
linearly reductive groups,
Reynolds operator,
rational $G$-spaces,
projective modules,
flat modules.

Received by editor(s):
February 20, 2004

Received by editor(s) in revised form:
May 30, 2004

Published electronically:
March 31, 2005

Communicated by:
Martin Lorenz

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.