Cleft comodules over Hopf quasigroups-Reference-Cited by-同舟云学术

Cleft comodules over Hopf quasigroups

Published:2015-10-29 Issue:06 Volume:17 Page:1550007
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

Álvarez J. N. Alonso¹,Vilaboa J. M. Fernández²,Rodríguez R. González³,Calvo C. Soneira⁴

Affiliation:

1. Departamento de Matemáticas, Universidad de Vigo, Campus Universitario Lagoas-Marcosende, E-36280 Vigo, Spain

2. Departamento de Departamento de Álxebra, Universidad de Santiago de Compostela, E-15771 Santiago de Compostela, Spain

3. Departamento de Matemática Aplicada II, Universidad de Vigo, Campus Universitario Lagoas-Marcosende, E-36310 Vigo, Spain

4. Departamento de Pedagoxía e Didáctica, Universidade da Coruña, Campus Universitario de Elviña, E-15007 A Coruña, Spain

Abstract

In this paper, we provide necessary and sufficient conditions for a cleft right H-comodule algebra (A, ϱA) over a Hopf quasigroup H to be isomorphic as an algebra to the crossed product AH♯σAHH, where AH is the coinvariants subalgebra of A and σAH is a morphism between H ⊗ H and AH. As a consequence, we obtain the corresponding version in the nonassociative setting of the result given by Blattner, Cohen and Montgomery for projections of Hopf algebras with coalgebra splitting. Concrete examples satisfying the obtained conditions are provided.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199715500078

Reference9 articles.

1. Crossed products and inner actions of Hopf algebras

2. Contributions to the theory of loops

3. Moufang loops of small order. I

4. Cleft comodule algebras for a bialgebra

5. Hopf quasigroups and the algebraic 7-sphere

Cited by 9 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Faithfully flat descent for magmas;Journal of Pure and Applied Algebra;2020-02

2. Multiplication Alteration by Two-Cocycles: The Non-associative Version;Bulletin of the Malaysian Mathematical Sciences Society;2020-01-07

3. Fundamental Theorems of Doi–Hopf Modules in a Nonassociative Setting;Bulletin of the Malaysian Mathematical Sciences Society;2018-04-16

4. Cleft extensions for quasi-entwining structures;Mathematica Slovaca;2018-03-31

5. Weak quasi-entwining structures;Filomat;2018