Hopf Modules and Yetter - Drinfel′d Modules
نویسندگان
چکیده
منابع مشابه
Yetter-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...
متن کاملYetter-drinfeld Modules for Turaev Crossed Structures
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 کاملDeformation cohomology for Yetter-Drinfel’d modules and Hopf (bi)modules
If A is a bialgebra over a field k, a left-right Yetter-Drinfel’d module over A is a k-linear space M which is a left A-module, a right A-comodule and such that a certain compatibility condition between these two structures holds. YetterDrinfel’d modules were introduced by D. Yetter in [18] under the name of “crossed bimodules” (they are called “quantum Yang-Baxter modules” in [5]; the present ...
متن کاملYetter-drinfeld Modules over Weak Hopf Algebras and the Center Construction
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1994
ISSN: 0021-8693
DOI: 10.1006/jabr.1994.1314