Related papers: Quantized function algebras at $q=0$: type $A_{n}$…

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 $C(SU_{0}(n+1))$…

The paper introduces a (universal) C*-algebra of continuous functions vanishing at infinity on the n-dimensional quantum complex space. To this end, the well-behaved Hilbert space representations of the defining relations are classified.…

The well-behaved representations of the coordinate algebra of a 2-dimensional quantum complex plane are classified and a C*-algebra is defined which can be viewed as the algebra of continuous functions on the 2-dimensional quantum complex…

The crystal limit C(K0) of the $q$-family of C*-algebras C(Kq) was introduced by Giri & Pal for all K=SU(n+1), n\geq 2. This article aims to prove that the crystal limits C(K0) have the property that the representations of C(Kq) give rise…

We study a deformation of the Cuntz-Toeplitz $C^*$-algebra determined by the relations $a_i^*a_i=1+q a_ia_i^*, a_i^*a_j=0$. We define well-behaved unbounded *-representations of the *-algebra defined by relations above and classify all such…

The so called quantized algebras of functions on affine Hecke algebras of type A and the corresponding q-Schur algebras are defined and their irreducible unitarizable representations are classified.

For a certain class of Lie bialgebras $(A,A^*)$ the corresponding quantum universal enveloping algebras $U_q(A)$ are prooved to be equivalent to quantum groups Fun$_q(F^*)$, $F^*$ being the factor group for the dual group $G^*$. This…

Let G be a simply connected semisimple compact Lie group with standard Poisson structure, K a closed Poisson-Lie subgroup, 0<q<1. We study a quantization C(G_q/K_q) of the algebra of continuous functions on G/K. Using results of Soibelman…

We develop a method to give presentations of quantized function algebras of complex reductive groups. In particular, we give presentations of quantized function algebras of automorphism groups of finite dimensional simple complex Lie…

The concept of quantization consists in replacing commutative quantities by noncommutative ones. In mathematical language an algebra of continuous functions on a locally compact topological space is replaced with a noncommutative…

S. L. Woronowicz's theory of introducing C*-algebras generated by unbounded elements is applied to q-normal operators satisfying the defining relation of the quantum complex plane. The unique non-degenerate C*-algebra of bounded operators…

It is shown that the algebra of continuous functions on the quantum $2n+1$-dimensional lens space $C(L^{2n+1}_q(N; m_0,\ldots, m_n))$ is a graph $C^*$-algebra, for arbitrary positive weights $ m_0,\ldots, m_n$. The form of the corresponding…

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 show that a C*-algebra generated by an irreducible representation of a finitely generated virtually nilpotent group satisfies the universal coefficient theorem and has real rank 0. This combines with previous joint work with Gillaspy and…

Let g be a simple Lie algebra and q transcendental. We consider the category C_P of finite-dimensional representations of the quantum loop algebra Uq(Lg) in which the poles of all l-weights belong to specified finite sets P. Given the data…

We prove a triangular decomposition theorem for the lower crystal lattice $\mathcal{O}_{t}^{A_{0}}(G)$ of the quantized function algebra $\mathcal{O}_{t}(G)$, where $G$ is a connected simply connected complex Lie group with Lie algebra…

The Ahtekar-Isham C*-algebra known from Loop Quantum Gravity is the algebra of continuous functions on the space of (generalized) connections with a compact structure Lie group. The algebra can be constructed by some inductive techniques…

We give a definition of partition C*-algebras: To any partition of a finite set, we assign algebraic relations for a matrix of generators of a universal C*-algebra. We then prove how certain relations may be deduced from others and we…

Quantum Lie algebras are generalizations of Lie algebras whose structure constants are power series in $h$. They are derived from the quantized enveloping algebras $\uqg$. The quantum Lie bracket satisfies a generalization of antisymmetry.…

We prove the existence of a strict deformation quantization for the canonical Poisson structure on the dual of an integrable Lie algebroid. It follows that any Lie groupoid C*-algebra may be regarded as a result of a quantization procedure.…