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
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.

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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.

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D. Radford, The structure of Hopf algebras with a projection, J. Algebra, 92 (1985), 322-347. doi: 10.1016/0021-8693(85)90124-3.

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Y. Doi, Hopf modules in Yetter-Drinfeld categories, Comm. Algebra, 26 (1998), 3057-3070. doi: 10.1080/00927879808826327.

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P. Schauenburg, Hopf modules and Yetter-Drinfel'd modules, J. Algebra, 169 (1994), 874-890.

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Y. Sommerhäuser, "Yetter-Drinfeld Hopf Algebras over Groups of Prime Order," Lecture Notes in Math, Vol. 1789, Springer, Berlin, 2002.

show all references

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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