Quantum Doubles from a Class of Noncocommutative Weak Hopf Algebras

Details Quantum Doubles from a Class of Noncocommutative Weak Hopf Algebras Quantum Doubles from a Class of Noncocommutative Weak Hopf Algebras

2004-05-08

arxiv.org/abs/math/0405145v1

J. Math. Phys. 45 (2004), 3266--3281

Mathematics

Quantum Algebra

LaTex 18 pages, to appear in J. Math. Phys. (To compile, need pb-diagram.sty, pb-lams.sty, pb-xy.sty and lamsarrow.sty)

Scientific paper

10.1063/1.1767989

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.

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