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On Frobenius and separable Galois cowreaths

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Abstract

We show that a Galois cowreath (A, X) in a monoidal category \({\mathcal {C}}\) is Frobenius if and only if the subalgebra of coinvariants \(A^{\mathrm{co}(X)}\hookrightarrow A\) is a Frobenius algebra extension in \({\mathcal {C}}\). Then we give necessary and sufficient conditions for \(A^{\mathrm{co}(X)}\hookrightarrow A\) to be separable, and prove that a Frobenius Galois cowreath is separable if and only if it admits a total integral.

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Acknowledgements

The authors are very grateful to the referee for the careful reading of the paper and valuable suggestions and comments.

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Authors and Affiliations

  1. Faculty of Mathematics and Informatics, University of Bucharest, Str. Academiei 14, 010014, Bucharest 1, Romania

    D. Bulacu

  2. Department of Mathematics, Universidad de Almería, 04071, Almería, Spain

    B. Torrecillas

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  1. D. Bulacu
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  2. B. Torrecillas
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Correspondence to B. Torrecillas.

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Work supported by the project MTM2017-86987-P “Anillos, modulos y algebra de Hopf”. 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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Bulacu, D., Torrecillas, B. On Frobenius and separable Galois cowreaths. Math. Z. 297, 25–57 (2021). https://doi.org/10.1007/s00209-020-02495-8

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