Quantum Double for Quasi-hopf Algebras

The quantum double for quasitriangular quasi-Hopf algebras

Let D(H) be the quantum double associated to a finite dimensional quasi-Hopf algebra H, as in [9] and [10]. In this note, we first generalize a result of Majid [15] for Hopf algebras, and then prove that the quantum double of a finite dimensional quasitriangular quasi-Hopf algebra is a biproduct in the sense of [4].

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...

Adjunctions between Hom and Tensor as endofunctors of (bi-) module category of comodule algebras over a quasi-Hopf algebra.

For a Hopf algebra H over a commutative ring k and a left H-module V, the tensor endofunctors V k - and - kV are left adjoint to some kinds of  Hom-endofunctors of _HM. The units and counits of these adjunctions are formally trivial as in the classical case.The category of (bi-) modules over a quasi-Hopf algebra is monoidal and some generalized versions of  Hom-tensor relations have been st...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

Generalized quantum current algebras

Two general families of new quantum deformed current algebras are proposed and identified both as infinite Hopf family of algebras, a structure which enable one to define “tensor products” of these algebras. The standard quantum affine algebras turn out to be a very special case of both algebra families, in which case the infinite Hopf family structure degenerates into standard Hopf algebras. T...