The structure theorems for Yetter-Drinfeld comodule algebras

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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

Abstract
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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 $A$.

Keywords: the structure theorem., Yetter-Drinfeld comodule algebra, Yetter-Drinfeld Hopf bimodule.

Mathematics Subject Classification: Primary: 16W3.

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

References:

[1]	L. B. Li and P. Zhang, Twisted Hopf algebras, Ringel-Hall algebras, and Green's categories, J. Algebra, 231 (2000), 713-743. doi: 10.1006/jabr.2000.8362.
[2]	S. Montgomery, "Hopf Algebras and Their Actions on Rings," CBMS Regional Conference Series in Mathematics, 82, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1993.
[3]	D. Radford, The structure of Hopf algebras with a projection, J. Algebra, 92 (1985), 322-347. doi: 10.1016/0021-8693(85)90124-3.
[4]	Y. Doi, Hopf modules in Yetter-Drinfeld categories, Comm. Algebra, 26 (1998), 3057-3070. doi: 10.1080/00927879808826327.
[5]	P. Schauenburg, Hopf modules and Yetter-Drinfel'd modules, J. Algebra, 169 (1994), 874-890.
[6]	Y. Sommerhäuser, "Yetter-Drinfeld Hopf Algebras over Groups of Prime Order," Lecture Notes in Math, Vol. 1789, Springer, Berlin, 2002.

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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), 713-743. doi: 10.1006/jabr.2000.8362.
[2]	S. Montgomery, "Hopf Algebras and Their Actions on Rings," CBMS Regional Conference Series in Mathematics, 82, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1993.
[3]	D. Radford, The structure of Hopf algebras with a projection, J. Algebra, 92 (1985), 322-347. doi: 10.1016/0021-8693(85)90124-3.
[4]	Y. Doi, Hopf modules in Yetter-Drinfeld categories, Comm. Algebra, 26 (1998), 3057-3070. doi: 10.1080/00927879808826327.
[5]	P. Schauenburg, Hopf modules and Yetter-Drinfel'd modules, J. Algebra, 169 (1994), 874-890.
[6]	Y. Sommerhäuser, "Yetter-Drinfeld Hopf Algebras over Groups of Prime Order," Lecture Notes in Math, Vol. 1789, Springer, Berlin, 2002.

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