Related papers: $C(SO_q(4)/SO_q(2))$ as a Groupoid $C^*$-algebra

We discuss necessary conditions for a compact quantum group to act on the algebra of noncommutative $n$-torus $\mathbb{T}_\theta^n$ in a filtration preserving way in the sense of Banica and Skalski. As a result, we construct a family of…

Let S be the Stone space of a complete, non-atomic Boolean algebra. Let G be a countably infinite group of homeomorphisms of S. Let the action of G on S have a free dense orbit. Then we prove that, on a generic subset of S, the orbit…

An algebra homomorphism $\psi$ from the nonstandard q-deformed (cyclically symmetric) algebra $U_q(so_3)$ to the extension ${\hat U}_q(sl_2)$ of the Hopf algebra $U_q(sl_2)$ is constructed. Not all irreducible representations of $U_q(sl_2)$…

A classification result is obtained for the C*-algebras that are (stably isomorphic to) inductive limits of 1-dimensional noncommutative CW complexes with trivial $K_1$-group. The classifying functor Cu is defined in terms of the Cuntz…

We prove that all finitely generated fully residually free groups (limit groups) have a sequence of finite dimensional unitary representations that `strongly converge' to the regular representation of the group. The corresponding statement…

We study Deaconu-Renault groupoids corresponding to surjective local homeomorphisms on locally compact, Hausdorff, second countable, totally disconnected spaces, and we characterise when the C*-algebras of these groupoids are AF embeddable.…

We develop a theory of graph C*-algebras using path groupoids and inverse semigroups. Row finiteness is not assumed so that the theory applies to graphs for which there are vertices emitting a countably infinite set of edges. We show that…

Given a locally compact group $G$ and a unitary representation $\rho:G\to U({\mathcal H})$ on a Hilbert space ${\mathcal H}$, we construct a $C^*$-correspondence ${\mathcal E}(\rho)={\mathcal H}\otimes_{\mathbb C} C^*(G)$ over $C^*(G)$ and…

We obtain partial affirmative answers to the question whether isomorphism of the unitary groups of two C*-algebras, either as topological groups or as discrete groups, implies isomorphism of the C*-algebras as real C*-algebras.

Let A be a separable unital nuclear purely infinite simple C*-algebra satisfying the Universal Coefficient Theorem, and such that the K_0-class of the identity is zero. We prove that every automorphism of order two of the K-theory of A is…

Let G=SU(2) and let \Omega G denote the space of continuous based loops in G, equipped with the pointwise conjugation action of G. It is a classical fact in topology that the ordinary cohomology H^*(\Omega G) is a divided polynomial algebra…

For all transcendental parameters, the irrational rotation algebra is shown to contain infinitely many C*-subalgebras satisfying the following properties. Each subalgebra is isomorphic to a direct sum of two matrix algebras of the same…

Let \alpha:G --> G be an endomorphism of a discrete amenable group such that [G:\alpha(G)]<infinity. We study the structure of the C^* algebra generated by the left convolution operators acting on the left regular representation space,…

Suppose $\mathcal{G}$ is a second-countable locally compact Hausdorff \'{e}tale groupoid, $G$ is a discrete group containing a unital subsemigroup $P$, and $c:\mathcal{G}\rightarrow G$ is a continuous cocycle. We derive conditions on the…

We solve a class of lifting problems involving approximate polynomial relations (soft polynomial relations). Various associated C*-algebras are therefore projective. The technical lemma we need is a new manifestation of Akemann and…

We study the natural representation of the topological full group of an ample Hausdorff groupoid in the groupoid's complex Steinberg algebra and in its full and reduced C*-algebras. We characterise precisely when this representation is…

We present a uniqueness theorem for the reduced C*-algebra of a twist $\mathcal{E}$ over a Hausdorff \'etale groupoid $\mathcal{G}$. We show that the interior $\mathcal{I}^\mathcal{E}$ of the isotropy of $\mathcal{E}$ is a twist over the…

Given a discrete and countable inverse semigroup $S$ one can study, in analogy to the group case, its geometric aspects. In particular, we can equip $S$ with a natural metric, given by the path metric in the disjoint union of its…

In this paper, we introduce C*-algebraic partial compact quantum groups, which are quantizations of topological groupoids with discrete object set and compact morphism spaces. These C*-algebraic partial compact quantum groups are…

We define and study large and stably large subalgebras of simple unital C*-algebras. The basic example is the orbit breaking subalgebra of a crossed product by Z, as follows. Let X be an infinite compact metric space, let h be a minimal…