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/AH separable and AH 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 (AH), thus generalizing the work of Alfaro and Szeto for H a group algebra. We also study Galois bases and Hirata systems.
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Communicated by S. Montgomery
1991 Mathematics Subject Classification: 16W30, 16H05
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Ouyang, M. Azumaya Extensions and Galois Correspondence. Algebra Colloq. 7, 43–57 (2000). https://doi.org/10.1007/s10011-000-0043-z
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DOI: https://doi.org/10.1007/s10011-000-0043-z