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Keywords = smash coproduct

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15 pages, 306 KB  
Article
A Morita-Takeuchi Context and Hopf Coquasigroup Galois Coextensions
by Huaiwen Guo and Shuanhong Wang
Symmetry 2023, 15(2), 551; https://doi.org/10.3390/sym15020551 - 18 Feb 2023
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Abstract
For H a Hopf quasigroup and C, a left quasi H-comodule coalgebra, we show that the smash coproduct CH (as a symmetry of smash product) is linked to some quotient coalgebra Q=C/CH*+ [...] Read more.
For H a Hopf quasigroup and C, a left quasi H-comodule coalgebra, we show that the smash coproduct CH (as a symmetry of smash product) is linked to some quotient coalgebra Q=C/CH*+ by a Morita-Takeuchi context (as a symmetry of Morita context). We use the Morita-Takeuchi setting to prove that for finite dimensional H, equivalent conditions for C/Q to be a Hopf quasigroup Galois coextension (as a symmetry of Galois extension). In particular, we consider a special case of quasigroup graded coalgebras as an application of our theory. Full article
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