# American Institute of Mathematical Sciences

2013, 20: 31-42. doi: 10.3934/era.2013.20.31

## The structure theorems for Yetter-Drinfeld comodule algebras

 1 Department of Mathematics and Information, Ludong University, Yantai, Shandong 264025, China

Received  September 2012 Revised  January 2013 Published  March 2013

In this paper, we first introduce the notion of a Yetter-Drinfeld comodule algebra and give examples. Then we give the structure theorems of Yetter-Drinfeld comodule algebras. That is, if $L$ is a Yetter-Drinfeld Hopf algebra and $A$ is a right $L$-Yetter-Drinfeld comodule algebra, then there exists an algebra isomorphism between $A$ and $A^{coL} \mathbin{\sharp} H$, where $A^{coL}$ is the coinvariant subalgebra of $A$.
Citation: Ling Jia. The structure theorems for Yetter-Drinfeld comodule algebras. Electronic Research Announcements, 2013, 20: 31-42. doi: 10.3934/era.2013.20.31
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##### References:
 [1] L. B. Li and P. Zhang, Twisted Hopf algebras, Ringel-Hall algebras, and Green's categories,, J. Algebra, 231 (2000), 713.  doi: 10.1006/jabr.2000.8362.  Google Scholar [2] S. Montgomery, "Hopf Algebras and Their Actions on Rings,", CBMS Regional Conference Series in Mathematics, 82 (1993).   Google Scholar [3] D. Radford, The structure of Hopf algebras with a projection,, J. Algebra, 92 (1985), 322.  doi: 10.1016/0021-8693(85)90124-3.  Google Scholar [4] Y. Doi, Hopf modules in Yetter-Drinfeld categories,, Comm. Algebra, 26 (1998), 3057.  doi: 10.1080/00927879808826327.  Google Scholar [5] P. Schauenburg, Hopf modules and Yetter-Drinfel'd modules,, J. Algebra, 169 (1994), 874.   Google Scholar [6] Y. Sommerhäuser, "Yetter-Drinfeld Hopf Algebras over Groups of Prime Order,", Lecture Notes in Math, (1789).   Google Scholar
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