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ON GORENSTEINNESS OF HOPF MODULE ALGEBRAS

Part of: Hopf algebras, quantum groups and related topics

Published online by Cambridge University Press:  10 June 2016

SERGE SKRYABIN
SERGE SKRYABIN*
Affiliation:
Institute of Mathematics and Mechanics, Kazan Federal University, Kremlevskaya St. 18, 420008 Kazan, Russia e-mail: Serge.Skryabin@kpfu.ru
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Abstract

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Let H be a Hopf algebra with a bijective antipode, A an H-simple H-module algebra finitely generated as an algebra over the ground field and module-finite over its centre. The main result states that A has finite injective dimension and is, moreover, Artin–Schelter Gorenstein under the additional assumption that each H-orbit in the space of maximal ideals of A is dense with respect to the Zariski topology. Further conclusions are derived in the cases when the maximal spectrum of A is a single H-orbit or contains an open dense H-orbit.

MSC classification

Primary: 16T05: Hopf algebras and their applications
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 59 , Issue 2 , May 2017 , pp. 299 - 321
Copyright
Copyright © Glasgow Mathematical Journal Trust 2016 

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