Examples of equivalences of Doi-Koppinen Hopf module categories, including Yetter-Drinfeld modules
نویسندگان
چکیده
منابع مشابه
Doi-Koppinen Hopf Modules Versus Entwined Modules
A Hopf module is an A-module for an algebra A as well as a C-comodule for a coalgebra C, satisfying a suitable compatibility condition between the module and comodule structures. To formulate the compatibility condition one needs some kind of interaction between A and C. The most classical case arises when A = C =: H is a bialgebra. Many subsequent variants of this were unified independently by...
متن کاملYetter-drinfeld Modules over Weak Bialgebras
We discuss properties of Yetter-Drinfeld modules over weak bialgebras over commutative rings. The categories of left-left, left-right, right-left and right-right Yetter-Drinfeld modules over a weak Hopf algebra are isomorphic as braided monoidal categories. Yetter-Drinfeld modules can be viewed as weak Doi-Hopf modules, and, a fortiori, as weak entwined modules. If H is finitely generated and p...
متن کاملYetter-drinfeld Modules under Cocycle Twists
We give an explicit formula for the correspondence between simple Yetter-Drinfeld modules for certain finite-dimensional pointed Hopf algebras H and those for cocycle twists H of H. This implies an equivalence between modules for their Drinfeld doubles. To illustrate our results, we consider the restricted two-parameter quantum groups ur,s(sln) under conditions on the parameters guaranteeing th...
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We provide an analog of the Joyal-Street center construction and of the Kassel-Turaev categorical quantum double in the context of the crossed categories introduced by Turaev. Then, we focus or attention to the case of categories of representation. In particular, we introduce the notion of a YetterDrinfeld module over a crossed group coalgebra H and we prove that both the category of Yetter-Dri...
متن کاملSemisimplicity of the Categories of Yetter-drinfeld Modules and Long Dimodules
Let k be a field, and H a Hopf algebra with bijective antipode. If H is commutative, noetherian, semisimple and cosemisimple, then the category HYD H of Yetter-Drinfeld modules is semisimple. We also prove a similar statement for the category of Long dimodules, without the assumption that H is commutative.
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ژورنال
عنوان ژورنال: Bulletin of the Belgian Mathematical Society - Simon Stevin
سال: 1999
ISSN: 1370-1444
DOI: 10.36045/bbms/1103149970