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Article overview
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Quantum Doubles from a Class of Noncocommutative Weak Hopf Algebras | Fang Li
; Yao-Zhong Zhang
; | Date: |
8 May 2004 | Journal: | J. Math. Phys. 45 (2004), 3266--3281 | Subject: | Quantum Algebra; Rings and Algebras; Mathematical Physics | math.QA math-ph math.MP math.RA | 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. | Source: | arXiv, math.QA/0405145 | Services: | Forum | Review | PDF | Favorites |
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