Quantum Doubles from a Class of Noncocommutative Weak Hopf Algebras
Abstract
The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products are constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which are generalizations of the Hopf pairs introduced by Takeuchi. As a special case, the quantum double of a finite dimensional biperfect (noncocommutative) weak Hopf algebra is built. Examples of quantum doubles from a Clifford monoid as well as a noncommutative and noncocommutative weak Hopf algebra are given, generalizing quantum doubles from a group and a noncommutative and noncocommutative Hopf algebra, respectively. Moreover, some characterisations of quantum doubles of finite dimensional biperfect weak Hopf algebras are obtained.
Keywords
Cite
@article{arxiv.math/0405145,
title = {Quantum Doubles from a Class of Noncocommutative Weak Hopf Algebras},
author = {Fang Li and Yao-Zhong Zhang},
journal= {arXiv preprint arXiv:math/0405145},
year = {2009}
}
Comments
LaTex 18 pages, to appear in J. Math. Phys. (To compile, need pb-diagram.sty, pb-lams.sty, pb-xy.sty and lamsarrow.sty)