Cleft comodules over Hopf quasigroups

被引：8
|
作者：
Alonso Alvarez, J. N. [1 ]
Fernandez Vilaboa, J. M. [2 ]
Gonzalez Rodriguez, R. [3 ]
Soneira Calvo, C. [4 ]
机构：
[1] Univ Vigo, Dept Matemat, E-36280 Vigo, Spain
[2] Univ Santiago de Compostela, Dept Alxebra, E-15771 Santiago De Compostela, Spain
[3] Univ Vigo, Dept Matemat Aplicada 2, E-36310 Vigo, Spain
[4] Univ A Coruna, Dept Pedag & Didact, E-15007 La Coruna, Spain
来源：
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2015年 / 17卷 / 06期
关键词：
Hopf quasigroup; cleft comodule algebra; crossed product; nonassociative algebra; ALGEBRAS; LOOPS;
D O I：
10.1142/S0219199715500078
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we provide necessary and sufficient conditions for a cleft right H-comodule algebra (A, rho(A)) over a Hopf quasigroup H to be isomorphic as an algebra to the crossed product A(H)sigma(AH) H, where A(H) is the coinvariants subalgebra of A and sigma(AH) is a morphism between H circle times H and A(H). 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.
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页数：20
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