منابع مشابه
Doi-Hopf Modules over Weak Hopf Algebras
The theory of Doi-Hopf modules [7, 10] is generalized to Weak Hopf Algebras [1, 12, 2].
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We replace the group of group-like elements of the quantized enveloping algebra Uq(g) of a finite dimensional semisimple Lie algebra g by some regular monoid and get the weak Hopf algebra w q (g). It is a new subclass of weak Hopf algebras but not Hopf algebras. Then we devote to constructing a basis of w q (g) and determine the group of weak Hopf algebra automorphisms of w q (g) when q is not ...
متن کاملA Class of Weak Hopf Algebras
Copyright q 2010 Dongming Cheng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We introduce a class of noncommutative and noncocommutative weak Hopf algebras with infinite Ext quivers and study their structure. We decompose them...
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We give a detailed comparison between the notion of a weak Hopf algebra (also called a quantum groupoid by Nikshych and Văınerman), and that of a ×R-bialgebra due to Takeuchi (and also called a bialgebroid or quantum (semi)groupoid by Lu and Xu). A weak bialgebra is the same thing as a ×R-bialgebra in which R is Frobenius-separable. We extend the comparison to cover module and comodule theory, ...
متن کاملWeak C-Hopf Algebras and Multiplicative Isometries
We show how the data of a finite dimensional weak C∗-Hopf algebra can be encoded into a pair (H, V ) where H is a finite dimensional Hilbert space and V :H⊗H → H⊗H is a partial isometry satisfying, among others, the pentagon equation. In case of V being unitary we recover the Baaj-Skandalis multiplicative unitary of the discrete compact type. Relation to the pseudomultiplicative unitary approac...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1999
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.7984