Frobenius and separable functors for the category of entwined modules over cowreaths, I: General theory

Daniel Bulacu; Stefaan Caenepeel; Blas Torrecillas

doi:10.1007/s10468-019-09884-6

Frobenius and separable functors for the category of entwined modules over cowreaths, I: General theory

Daniel Bulacu, Stefaan Caenepeel, Blas Torrecillas

Mathematics-TW

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10 Citations (Scopus)

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Abstract

Entwined modules over cowreaths in a monoidal category are introduced. They can be identified to coalgebras in an appropriate monoidal category. It is investigated when such coalgebras are Frobenius (resp. separable), and when the forgetful functor from entwined modules to representations of the underlying algebra is Frobenius (resp. separable). These properties are equivalent when the unit object of the category is a ⊗-generator.

Original language	English
Pages (from-to)	1119-1157
Number of pages	39
Journal	Algebras and Representation Theory
Volume	23
Issue number	3
DOIs	https://doi.org/10.1007/s10468-019-09884-6
Publication status	Published - 1 Jun 2020

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© 2019, Springer Nature B.V.

Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

Keywords

Module category
cowreath
entwined module
Frobenius functor
separable functor
Frobenius coalgebra
oseparable coalgebra

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AB - Entwined modules over cowreaths in a monoidal category are introduced. They can be identified to coalgebras in an appropriate monoidal category. It is investigated when such coalgebras are Frobenius (resp. separable), and when the forgetful functor from entwined modules to representations of the underlying algebra is Frobenius (resp. separable). These properties are equivalent when the unit object of the category is a ⊗-generator.

KW - Module category

KW - cowreath

KW - entwined module

KW - Frobenius functor

KW - separable functor

KW - Frobenius coalgebra

KW - oseparable coalgebra

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JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

IS - 3

ER -

Frobenius and separable functors for the category of entwined modules over cowreaths, I: General theory

Abstract

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Keywords

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