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

Wiskunde-TW

Onderzoeksoutput: Article › peer review

8 Citaten (Scopus)

11 Downloads (Pure)

Samenvatting

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.

Originele taal-2	English
Pagina's (van-tot)	1119-1157
Aantal pagina's	39
Tijdschrift	Algebras and Representation Theory
Volume	23
Nummer van het tijdschrift	3
DOI's	https://doi.org/10.1007/s10468-019-09884-6
Status	Published - 1 jun 2020

Bibliografische nota

Publisher Copyright:
© 2019, Springer Nature B.V.

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

Toegang tot document

10.1007/s10468-019-09884-6

Andere bestanden en links

Link to publication in Scopus

Citeer dit

@article{2538583b014b4aeeb4e5a28f741fe021,

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

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.",

keywords = "Module category, cowreath, entwined module, Frobenius functor, separable functor, Frobenius coalgebra, oseparable coalgebra",

author = "Daniel Bulacu and Stefaan Caenepeel and Blas Torrecillas",

year = "2020",

month = jun,

day = "1",

doi = "10.1007/s10468-019-09884-6",

language = "English",

volume = "23",

pages = "1119--1157",

journal = "Algebras and Representation Theory",

issn = "1386-923X",

publisher = "Springer Netherlands",

number = "3",

}

TY - JOUR

T1 - Frobenius and separable functors for the category of entwined modules over cowreaths, I: General theory

AU - Bulacu, Daniel

AU - Caenepeel, Stefaan

AU - Torrecillas, Blas

PY - 2020/6/1

Y1 - 2020/6/1

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=85064484764&partnerID=8YFLogxK

U2 - 10.1007/s10468-019-09884-6

DO - 10.1007/s10468-019-09884-6

M3 - Article

VL - 23

SP - 1119

EP - 1157

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

SN - 1386-923X

IS - 3

ER -

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

Samenvatting

Bibliografische nota

Toegang tot document

Andere bestanden en links

Vingerafdruk

Citeer dit