Biperfect Hopf Algebras

Baxter Algebras and Hopf Algebras

George E. Andrews Department of Mathematics Pennsylvania State University University Park, PA 16802, USA ([email protected]) Li Guo Department of Mathematics and Computer Science Rutgers University at Newark Newark, NJ 07102, USA ([email protected]) William Keigher Department of Mathematics and Computer Science Rutgers University at Newark Newark, NJ 07102, USA ([email protected]...

Braided Hopf Algebras Obtained from Coquasitriangular Hopf Algebras

Let (H, σ) be a coquasitriangular Hopf algebra, not necessarily finite dimensional. Following methods of Doi and Takeuchi, which parallel the constructions of Radford in the case of finite dimensional quasitriangular Hopf algebras, we define Hσ , a sub-Hopf algebra of H, the finite dual of H. Using the generalized quantum double construction and the theory of Hopf algebras with a projection, we...

Cohomology of Hopf C-algebras and Hopf von Neumann algebras

We will define two canonical cohomology theories for Hopf C∗-algebras and for Hopf von Neumann algebras (with coefficients in their comodules). We will then study the situations when these cohomologies vanish. The cases of locally compact groups and compact quantum groups will be considered in more details. 1991 AMS Mathematics Classification number: Primary: 46L55, 46L05; Secondary: 43A07, 22D25

Quantum Doubles From A Class Of Noncocommutative Weak Hopf Algebras

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 a...

On the Coderivations of Some Hopf Algebras