Related papers: Unbounded representations of $q$-deformation of Cu…
For $C^*$-algebra generated by a finite family of isometries $s_j$, $j=1,\dots,d$ satisfying $q_{ij}$-commutation relations \[ s_j^* s_j = I, \quad s_j^* s_k = q_{ij}s_ks_j^*, \qquad q_{ij} = \bar q_{ji}, |q_{ij}|<1, \ 1\le i \ne j \le d,…
We define the notion of quantized function algebras at $q=0$ or crystallization of the $q$ deformations of the type $A_{n}$ compact Lie groups at the $C^*$-algebra level. The $C^{*}$-algebra $A_{n}(0)$ is defined as a universal…
Crystallization of the $C^*$-algebras $C(SU_{q}(n+1))$ was introduced by Giri \& Pal as a $C^*$-algebra $C(SU_{0}(n+1))$ given by a finite set of generators and relations. Here we study representations of the $C^*$-algebra $C(SU_{0}(n+1))$…
A realization of a deformed Lorentz algebra is considered and its irreducible representations are found; in the limit $q\to 1$, these are precisely the irreducible representations of the classical Lorentz group.
A class of well-behaved *-representations of a q-deformed Heisenberg algebra is studied and classified.
The main aim of this paper is to give classes of irreducible infinite dimensional representations and of irreducible $*$-representations of the q-deformed algebra $U'_q(so_{2,2})$ which is a real form of the non-standard deformation…
The main purpose of this paper is to construct *-representations from unbounded C$^*$-seminorms on partial *-algebras and to investigate their *-representations.
A classification of finite dimensional irreducible representations of the nonstandard $q$-deformation $U'_q(so_n)$ of the universal enveloping algebra $U(so(n, C))$ of the Lie algebra $so(n, C)$ (which does not coincides with the…
For the nonstandard $q$-deformed algebras $U_q(so_n)$, defined recently in terms of trilinear relations for generating elements, most general finite dimensional irreducible representations directly corresponding to those of nondeformed…
We continue our study of Hilbert space representations of the Reflection Equation Algebra, again focusing on the algebra constructed from the $R$-matrix associated to the $q$-deformation of $GL(N,\mathbb{C})$ for $0<q<1$. We develop a form…
We investigate representations of *-algebras associated with posets. Unitarizable representations of the corresponding (bound) quivers (which are polystable representations for some appropriately chosen slope function) give rise to…
The aim of this paper is to give a complete classification of irreducible finite dimensional representations of the nonstandard q-deformation U'_q(so(n)) (which does not coincide with the Drinfeld-Jimbo quantum algebra U_q(so(n)) of the…
We study the representation theory and enveloping $C^*$-algebras for Wick analogues of CAR and twisted CAR algebras. The realization of the $C^*$-algebras under consideration as algebras of continuous matrix-functions satisfying certain…
We introduce representations of the Cuntz algebra $\con$ which are parameterized by sequences in the set of unit vectors in ${\bf C}^{N}$. These representations are natural generalizations of permutative representations by…
We consider $C^*$-algebra $\mathcal{E}_{n,m}^q$, which is a $q$-twist of two Cuntz-Toeplitz algebras. For the case $|q|<1$ we give an explicit formula, which untwists the $q$-deformation, thus showing that the isomorphism class of…
We show that C*-algebras generated by irreducible representations of finitely generated nilpotent groups satisfy the universal coefficient theorem of Rosenberg and Schochet. This result combines with previous work to show that these…
In this paper we show that the universal C*-algebra satisfying the Cuntz-Li relations is generated by an inverse semigroup of partial isometries. We apply Exel's theory of tight representations to this inverse semigroup. We identify the…
The q-deformed algebra ${\rm so}'_q(r,s)$ is a real form of the q-deformed algebra $U'_q({\rm so}(n,\mathbb{C}))$, $n=r+s$, which differs from the quantum algebra $U_q({\rm so}(n,\mathbb{C}))$ of Drinfeld and Jimbo. We study representations…
Infinite dimensional representations of the real form U_q(u_{n,1}) of the Drinfeld--Jimbo algebra U_q(gl_{n+1}) are defined. The principal series of representations of U_q(u_{n,1}) is studied. Intertwining operators for pairs of the…
We study C*-irreducibility of inclusions of reduced twisted group C*-algebras and of reduced group C*-algebras. We characterize C*-irreducibility in the case of an inclusion arising from a normal subgroup, and exhibit many new examples of…