On Cleft Extensions of the Tensor Product of Two Hopf Algebras

被引：0

作者：

Yao, Ningyuan ^{[1
]}

Jiang, Xiaolong ^{[1
,2
]}

机构：

[1] Sun Yat Sen Univ, Sch Informat Sci & Technol, Guangzhou 510006, Guangdong, Peoples R China

[2] Sun Yat Sen Univ, Sch Math, Guangzhou 510006, Guangdong, Peoples R China

来源：

COMMUNICATIONS IN ALGEBRA | 2013年 / 41卷 / 11期

关键词：

Cleft extensions; Crossed systems; Hopf algebras; 16T15; CROSSED-PRODUCTS; COMODULE ALGEBRAS;

D O I：

10.1080/00927872.2012.695836

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we first decompose a cleft extension for X circle times Y into two cleft extensions for X and Y respectively, where X and Y are Hopf algebras on a commutative ring R. Conversely, we introduce the concept of consistent cleft Hopf extensions and prove that one can construct a cleft extension for X circle times Y by two cleft extensions for X and Y if and only if these two cleft extensions are consistent. An example is also given to show an application of our main results.

引用

页码：4299 / 4332

页数：34

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