{"title":"The structure theorems for Yetter-Drinfeld comodule algebras","authors":"Ling Jia","doi":"10.3934/ERA.2013.20.31","DOIUrl":null,"url":null,"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 $A$.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"20 1","pages":"31-42"},"PeriodicalIF":0.0000,"publicationDate":"2013-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Research Announcements in Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/ERA.2013.20.31","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
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 $A$.
本文首先引入了yeter - drinfeld模代数的概念，并给出了实例。然后给出了叶特-德林菲尔德模代数的结构定理。即，如果$L$是一个yeter - drinfeld Hopf代数，$ a $是一个右$L$- yeter - drinfeld模代数，则$ a $与$ a ^{coL} \mathbin{\sharp} H$之间存在代数同构，其中$ a ^{coL}$是$ a $的协不变子代数。
期刊介绍：
Electronic Research Archive (ERA), formerly known as Electronic Research Announcements in Mathematical Sciences, rapidly publishes original and expository full-length articles of significant advances in all branches of mathematics. All articles should be designed to communicate their contents to a broad mathematical audience and must meet high standards for mathematical content and clarity. After review and acceptance, articles enter production for immediate publication.
ERA is the continuation of Electronic Research Announcements of the AMS published by the American Mathematical Society, 1995—2007
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