Hopf Quasigroup Galois Extensions and a Morita Equivalence

For H, a Hopf coquasigroup, and A, a left quasi-H-module algebra, we show that the smash product A#H is linked to the algebra of H invariants AH by a Morita context. We use the Morita setting to prove that for finite dimensional H, there are equivalent conditions for A/AH to be Galois parallel in th...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-01, Vol.11 (2), p.273
Main Authors: Guo, Huaiwen, Wang, Shuanhong
Format: Article
Language:English
Subjects:
Algebra
Equivalence
Galois extension
Hopf (co)quasigroup
morita context
smash product
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Summary:For H, a Hopf coquasigroup, and A, a left quasi-H-module algebra, we show that the smash product A#H is linked to the algebra of H invariants AH by a Morita context. We use the Morita setting to prove that for finite dimensional H, there are equivalent conditions for A/AH to be Galois parallel in the case of H finite dimensional Hopf algebra.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11020273