scholarly journals Cleft extensions of a family of braided Hopf algebras

2016 ◽  
Vol 45 (7) ◽  
pp. 3166-3205
Author(s):  
Mauricio Da Rocha ◽  
Jorge A. Guccione ◽  
J. Guccione
Keyword(s):  
Hopf Algebras ◽  
Cleft Extensions

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 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 Two-cocycles and cleft extensions in left braided categories

2020 ◽  
pp. 2140013
Author(s):  
István Heckenberger ◽  
Kevin Wolf
Keyword(s):  
Hopf Algebra ◽  
Hopf Algebras ◽  
Drinfeld Module ◽  
Drinfeld Modules ◽  
Cleft Extensions ◽  
Braided Categories

We define two-cocycles and cleft extensions in categories that are not necessarily braided, but where specific objects braid from one direction, like for a Hopf algebra [Formula: see text] a Yetter–Drinfeld module braids from the left with [Formula: see text]-modules. We will generalize classical results to this context and give some application for the categories of Yetter–Drinfeld modules and [Formula: see text]-modules. In particular, we will describe liftings of coradically graded Hopf algebras in the category of Yetter–Drinfeld modules with these techniques.

On Cleft Extensions of the Tensor Product of Two Hopf Algebras

2013 ◽  
Vol 41 (11) ◽  
pp. 4299-4332
Author(s):  
Ningyuan Yao ◽  
Xiaolong Jiang
Keyword(s):  
Tensor Product ◽  
Hopf Algebras ◽  
Cleft Extensions

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 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.

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
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