The structure theorems for Yetter-Drinfeld comodule algebras
نویسندگان
چکیده
منابع مشابه
On Lie Algebras in the Category of Yetter - Drinfeld Modules
The category of Yetter-Drinfeld modules YD K over a Hopf algebra K (with bijektive antipode over a field k) is a braided monoidal category. If H is a Hopf algebra in this category then the primitive elements of H do not form an ordinary Lie algebra anymore. We introduce the notion of a (generalized) Lie algebra in YD K such that the set of primitive elements P (H) is a Lie algebra in this sense...
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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...
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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...
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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 introduce Yetter-Drinfeld modules over a weak Hopf algebra H, and show that the category of Yetter-Drinfeld modules is isomorphic to the center of the category of H-modules. The categories of left-left, left-right, right-left and right-right Yetter-Drinfeld modules are isomorphic as braided monoidal categories. Yetter-Drinfeld modules can be viewed as weak DoiHopf modules, and, a fortiori, a...
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ژورنال
عنوان ژورنال: Electronic Research Announcements in Mathematical Sciences
سال: 2013
ISSN: 1935-9179
DOI: 10.3934/era.2013.20.31