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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The Connes spectrum of group actions and group gradings for certain quotient rings


Authors: James Osterburg and Xue Yao
Journal: Trans. Amer. Math. Soc. 347 (1995), 2263-2275
MSC: Primary 16W30; Secondary 16S35, 16W50
DOI: https://doi.org/10.1090/S0002-9947-1995-1273514-5
MathSciNet review: 1273514
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Abstract: Let $ H$ be a finite-dimensional, semisimple Hopf algebra over an algebraically closed field $ K$ where $ H$ is either commutative or cocommutative. We let $ A$ be an $ H$-module algebra which is semiprime right Goldie. We show that the Connes spectrum of $ H$ acting on $ A$ is the Connes spectrum of $ H$ acting on the classical quotient ring of $ A$. In our last section, we define a symmetric quotient ring and show that the Connes spectrum of the ring and its quotient ring are the same. Finally, we apply our results to finite group actions and group gradings.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1995-1273514-5
Keywords: Connes spectrum, Hopf algebra actions, Goldie rings, symmetric quotient ring
Article copyright: © Copyright 1995 American Mathematical Society