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Frobenius cowreaths and Morita contexts

  • Daniel Bulacu ORCID logo and Blas Torrecillas ORCID logo EMAIL logo
Published/Copyright: June 11, 2020

Abstract

We prove a uniqueness type theorem for (weak, total) integrals on a Frobenius cowreath in a monoidal category. When the cowreath is, moreover, pre-Galois, we construct a Morita context relating the subalgebra of coinvariants and a certain wreath algebra. Then we see that the strictness of the Morita context is related to the Galois property of the cowreath and the existence of a weak total integral on it. We apply our results to quasi-Hopf algebras.

MSC 2010: 16T05; 18D10; 16S34

Communicated by Manfred Droste


Award Identifier / Grant number: MTM2017-86987-P

Funding statement: Work supported by the project MTM2017-86987-P “Anillos, modulos y algebra de Hopf”.

Acknowledgements

The first author thanks the University of Almeria (Spain) for its warm hospitality. The authors also thank Bodo Pareigis for sharing his “diagrams” program.

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Received: 2019-09-26
Revised: 2020-03-20
Published Online: 2020-06-11
Published in Print: 2020-09-01

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