The structure theorems for Yetter-Drinfeld comodule algebras

Ling Jia

doi:10.3934/era.2013.20.31

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

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The structure theorems for Yetter-Drinfeld comodule algebras

Ling Jia^1,

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

Received: August 31, 2012

Revised: December 31, 2012

Published: December 2012

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Abstract

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 $A$.

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Mathematics Subject Classification: Primary: 16W30.

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