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Azumaya Extensions and Galois Correspondence

Azumaya Extensions and Galois Correspondence For H a finite-dimensional Hopf algebra over a field k, we study H*-Galois Azumaya extensions A, i.e., A is an H-module algebra which is H*-Galois with A/A H separable and A H Azumaya. We prove that there is a Galois correspondence between a set of separable subalgebras of A and a set of separable subalgebras of C A (A H ), thus generalizing the work of Alfaro and Szeto for H a group algebra. We also study Galois bases and Hirata systems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Algebra Colloquium Springer Journals

Azumaya Extensions and Galois Correspondence

Ouyang, Min
Algebra Colloquium , Volume 7 (1) – Jan 1, 2000
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15 pages

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Publisher
Springer Journals
Copyright
Copyright © 2000 by Springer-Verlag Hong Kong
Subject
Mathematics; Algebra; Algebraic Geometry
ISSN
1005-3867
eISSN
0219-1733
DOI
10.1007/s10011-000-0043-z
Publisher site
See Article on Publisher Site

Abstract

For H a finite-dimensional Hopf algebra over a field k, we study H*-Galois Azumaya extensions A, i.e., A is an H-module algebra which is H*-Galois with A/A H separable and A H Azumaya. We prove that there is a Galois correspondence between a set of separable subalgebras of A and a set of separable subalgebras of C A (A H ), thus generalizing the work of Alfaro and Szeto for H a group algebra. We also study Galois bases and Hirata systems.

Journal

Algebra Colloquium – Springer Journals

Published: Jan 1, 2000

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