Thoma type results for discrete quantum groups

Rieffel Type Discrete Deformation of Finite Quantum Groups

We introduce a discrete deformation of Rieffel type for finite (quantum) groups. Using this, we give an example of a finite quantum group A of order 18 such that neither A nor its dual can be expressed as a crossed product of the form C(G1) ⋊τ G2 with G1 and G2 ordinary finite groups. We also give a deformation of finite groups of Lie type by using their maximal abelian subgroups.

Quasi-Discrete Locally Compact Quantum Groups

Let A be a C *-algebra. Let A ⊗ A be the minimal C *-tensor product of A with itself and let M (A ⊗ A) be the multiplier algebra of A ⊗ A. A comultiplication on A is a non-degenerate *-homomorphism ∆ : A → M (A ⊗ A) satisfying the coassociativity law (∆ ⊗ ι)∆ = (ι ⊗ ∆)∆ where ι is the identity map and where ∆ ⊗ ι and ι ⊗ ∆ are the unique extensions to M (A ⊗ A) of the obvious maps on A ⊗ A. We ...

Paragrassmann Integral, Discrete Systems and Quantum Groups

This report is based on review paper [1]. Some aspects of differential and integral calculi on generalized grassmann (paragrassmann) algebras are considered. The integration over paragrassmann variables is applied to evaluate the partition function for the Z p+1 Potts model on a chain. Finite dimensional paragrassmann representations for GL q (2) are constructed. Generalizations of grassmann al...

Matrix Quantum Groups of Type

To a Hecke symmetry R there associate the matrix bialgebra ER and the matrix Hopf algebra HR, which are called function rings on the matrix quantum semi-group and matrix quantum groups associated to R. We show that for an even Hecke symmetry, the rational representations of the corresponding quantum group are absolutely reducible and compute the integral on the function ring of the quantum grou...

Structural Properties of Inner Amenable Discrete Groups