Crossed products over weak Hopf algebras related to cleft extensions and cohomology

2014 ◽  
Vol 35 (2) ◽  
pp. 161-190 ◽  
Author(s):  
José Nicanor Alonso Álvarez ◽  
José Manuel Fernández Vilaboa ◽  
Ramón González Rodríguez
Keyword(s):  
Hopf Algebras ◽  
Crossed Products ◽  
Cleft Extensions ◽  
Weak Hopf Algebras

scholarly journals Comparison of two notions of weak crossed product

2020 ◽  
pp. 2150059
Author(s):  
Jorge A. Guccione ◽  
Juan J. Guccione
Keyword(s):  
Hopf Algebra ◽  
Hopf Algebras ◽  
Crossed Product ◽  
Weak Hopf Algebra ◽  
Crossed Products ◽  
Hopf Algebroid ◽  
Hopf Algebroids ◽  
Weak Crossed Product ◽  
Cleft Extensions ◽  
Weak Hopf Algebras

We compare the restriction to the context of weak Hopf algebras of the notion of crossed product with a Hopf algebroid introduced in [Cleft extensions of Hopf algebroids, Appl. Categor. Struct. 14(5–6) (2006) 431–469] with the notion of crossed product with a weak Hopf algebra introduced in [Crossed products for weak Hopf algebras with coalgebra splitting, J. Algebra 281(2) (2004) 731–752].

scholarly journals Crossed products for weak Hopf algebras with coalgebra splitting

2004 ◽  
Vol 281 (2) ◽  
pp. 731-752 ◽  
Author(s):  
J.N. Alonso Álvarez ◽  
R. González Rodríguez
Keyword(s):  
Hopf Algebras ◽  
Crossed Products ◽  
Weak Hopf Algebras

scholarly journals Cleft extensions of weak Hopf algebras

2020 ◽  
Vol 547 ◽  
pp. 668-710
Author(s):  
Jorge A. Guccione ◽  
Juan J. Guccione ◽  
Christian Valqui
Keyword(s):  
Hopf Algebras ◽  
Cleft Extensions ◽  
Weak Hopf Algebras

scholarly journals Weak quasi-entwining structures

Filomat ◽  
2018 ◽  
Vol 32 (18) ◽  
pp. 6229-6252
Author(s):  
Álvarez Alonso ◽  
Vilaboa Fernádez ◽  
González Rodríguez
Keyword(s):  
Galois Extension ◽  
Hopf Algebras ◽  
Normal Basis ◽  
Galois Extensions ◽  
Cleft Extension ◽  
Cleft Extensions ◽  
Weak Hopf Algebras

In this paper we introduce the notion of weak quasi-entwining structure as a generalization of quasi-entwining structures and weak entwining structures. Also, we formulate the notions of weak cleft extension, weak Galois extension, and weak Galois extension with normal basis associated to a weak quasientwining structure. Moreover, we prove that, under some suitable conditions, there exists an equivalence between weak Galois extensions with normal basis and weak cleft extensions. As particular instances, we recover some results previously proved for Hopf quasigroups, weak Hopf quasigroups and weak Hopf algebras.

On Weak Crossed Products of Weak Hopf Algebras

2011 ◽  
Vol 16 (3) ◽  
pp. 633-657 ◽  
Author(s):  
Ling Liu ◽  
Bing-liang Shen ◽  
Shuan-hong Wang
Keyword(s):  
Hopf Algebras ◽  
Crossed Products ◽  
Weak Hopf Algebras

scholarly journals Weak C-cleft extensions, weak entwining structures and weak Hopf algebras

2005 ◽  
Vol 284 (2) ◽  
pp. 679-704 ◽  
Author(s):  
J.N. Alonso Álvarez ◽  
J.M. Fernández Vilaboa ◽  
R. González Rodríguez ◽  
A.B. Rodríguez Raposo
Keyword(s):  
Hopf Algebras ◽  
Cleft Extensions ◽  
Weak Hopf Algebras

Crossed Products for Weak Hopf Algebras

2009 ◽  
Vol 37 (7) ◽  
pp. 2274-2289 ◽  
Author(s):  
Ana Belén Rodríguez Raposo
Keyword(s):  
Hopf Algebras ◽  
Crossed Products ◽  
Weak Hopf Algebras

A braided T-category over weak monoidal Hom-Hopf algebras

2019 ◽  
Vol 19 (08) ◽  
pp. 2050159
Author(s):  
Guohua Liu ◽  
Wei Wang ◽  
Shuanhong Wang ◽  
Xiaohui Zhang
Keyword(s):  
Hopf Algebra ◽  
Hopf Algebras ◽  
Weak Hopf Algebras ◽  
T Category

In this paper, we define and study weak monoidal Hom-Hopf algebras, which generalize both weak Hopf algebras and monoidal Hom-Hopf algebras. Let [Formula: see text] be a weak monoidal Hom-Hopf algebra with bijective antipode and let [Formula: see text] be the set of all automorphisms of [Formula: see text], we introduce a category [Formula: see text] with [Formula: see text] and construct a braided [Formula: see text]-category [Formula: see text] having all the categories [Formula: see text] as components.

scholarly journals Doi-hopf modules over weak hopf algebras

2000 ◽  
Vol 28 (10) ◽  
pp. 4687-4698 ◽  
Author(s):  
Gabriella Böhm
Keyword(s):  
Hopf Algebras ◽  
Hopf Modules ◽  
Weak Hopf Algebras
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