Cleft extensions of weak Hopf algebras

Jorge A. Guccione; Juan J. Guccione; Christian Valqui

doi:10.1016/j.jalgebra.2019.11.029

Cleft extensions of weak Hopf algebras

Jorge A. Guccione, Juan J. Guccione, Christian Valqui

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Abstract

In this paper we study the theory of cleft extensions for a weak bialgebra H. Among other results, we determine when two unitary crossed products of an algebra A by H are equivalent and we prove that if H is a weak Hopf algebra, then the categories of H-cleft extensions of an algebra A, and of unitary crossed products of A by H, are equivalent.

Original language	English
Pages (from-to)	668-710
Number of pages	43
Journal	Journal of Algebra
Volume	547
DOIs	https://doi.org/10.1016/j.jalgebra.2019.11.029
State	Published - 1 Apr 2020

Keywords

Cleft extension
Symmetric categories
Weak Hopf algebras
Weak crossed product

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10.1016/j.jalgebra.2019.11.029

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title = "Cleft extensions of weak Hopf algebras",

abstract = "In this paper we study the theory of cleft extensions for a weak bialgebra H. Among other results, we determine when two unitary crossed products of an algebra A by H are equivalent and we prove that if H is a weak Hopf algebra, then the categories of H-cleft extensions of an algebra A, and of unitary crossed products of A by H, are equivalent.",

keywords = "Cleft extension, Symmetric categories, Weak Hopf algebras, Weak crossed product",

author = "Guccione, {Jorge A.} and Guccione, {Juan J.} and Christian Valqui",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2020",

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doi = "10.1016/j.jalgebra.2019.11.029",

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AU - Guccione, Jorge A.

AU - Guccione, Juan J.

AU - Valqui, Christian

PY - 2020/4/1

Y1 - 2020/4/1

N2 - In this paper we study the theory of cleft extensions for a weak bialgebra H. Among other results, we determine when two unitary crossed products of an algebra A by H are equivalent and we prove that if H is a weak Hopf algebra, then the categories of H-cleft extensions of an algebra A, and of unitary crossed products of A by H, are equivalent.

AB - In this paper we study the theory of cleft extensions for a weak bialgebra H. Among other results, we determine when two unitary crossed products of an algebra A by H are equivalent and we prove that if H is a weak Hopf algebra, then the categories of H-cleft extensions of an algebra A, and of unitary crossed products of A by H, are equivalent.

KW - Cleft extension

KW - Symmetric categories

KW - Weak Hopf algebras

KW - Weak crossed product

UR - http://www.scopus.com/inward/record.url?scp=85076500319&partnerID=8YFLogxK

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DO - 10.1016/j.jalgebra.2019.11.029

M3 - Article

AN - SCOPUS:85076500319

SN - 0021-8693

VL - 547

SP - 668

EP - 710

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Cleft extensions of weak Hopf algebras

Abstract

Keywords

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