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.  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

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.  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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