Related papers: Compact metrizable structures and classification p…

This is the final one in the series of papers where we introduce and study the $C^*$-algebras associated with topological graphs. In this paper, we get a sufficient condition on topological graphs so that the associated $C^*$-algebras are…

We prove a number of results having to do with equipping type-I $\mathrm{C}^*$-algebras with compact quantum group structures, the two main ones being that such a compact quantum group is necessarily co-amenable, and that if the…

The principal aim of this paper is to give a dynamical presentation of the Jiang-Su algebra. Originally constructed as an inductive limit of prime dimension drop algebras, the Jiang-Su algebra has gone from being a poorly understood oddity…

We introduce a classification of locally compact Hausdorff topological spaces with respect to the behavior of $\sigma$-compact subsets, and relying on this classification we study properties of corresponding $C^*$-algebras in terms of frame…

It shown that an a locally injective surjection on a compact metric space admits a canonical locally homeomorphic extension such that the associated C*-algebras are isomorphic. This is then used in a study of the possible inverse…

For metrizable spaces we replace the notion of almost periodic homeomorphism with a similar notion and verify that the usual characterizations of almost periodic homeomorphisms of compact metric spaces are valid for all metrizable spaces.

We define a categorical framework in which we build a systematic construction that provides generic invariants for C*-algebras. The benefit is significant as we show that any invariant arising this way automatically enjoys nice properties…

We characterize relatively norm compact sets in the regular $C^*$-algebra of finitely generated Coxeter groups using a geometrically defined positive semigroup acting on the algebra.

I introduce yet another way to associate a C*-algebra to a graph and construct a simple nuclear C*-algebra that has irreducible representations both on a separable and a nonseparable Hilbert space.

Let $K$ be a compact metric space and let $\gamma = (\gamma_1, \dots, \gamma_n)$ be a system of proper contractions on $K$. We study a C*-algebra $\mathcal{MC}_{\gamma_1, \dots, \gamma_n}$ generated by all multiplication operators by…

A classification is given of certain separable nuclear C*-algebras not necessarily of real rank zero, namely the class of simple C*-algebras which are inductive limits of continuous-trace C*-algebras whose building blocks have their…

We study the elementary C*-algebra whose elements are the sum of a diagonal plus a compact operator. We describe the structure of the unitary group, the sets of ideals, automorhisms and projections.

We study locally compact metric spaces that enjoy various forms of homogeneity with respect to M\"obius self-homeomorphisms. We investigate connections between such homogeneity and the combination of isometric homogeneity with…

It is shown that if $A$ and $B$ are unital separable simple nuclear $\mathcal Z$-stable C$^*$-algebras and there is a unital embedding $A \rightarrow B$ which is invertible on $KK$-theory and traces, then $A \cong B$. In particular, two…

We introduce a compactification construction for abstract quasi-local C*-algebras over countable metric spaces equipped with an isometric group action which is functorial with respect to bounded spread isomorphisms. In $1$D, the…

We provide a uniform framework to study the exceptional homogeneous compact geometries of type C3. This framework is then used to show that these are simply connected, answering a question by Kramer and Lytchak, and to calculate the full…

We obtain a description of the C*-algebras which can occur as a simple quotient of the C*-algebra of a locally injective surjection on a compact metric space of finite covering dimension.

We define a notion of (one-sided) edge shift spaces associated to ultragraphs. In the finite case our notion coincides with the edge shift space of a graph. In general, we show that our space is metrizable and has a countable basis of…

A Hilbert $C^*$-quad module of finite type has a multi structure of Hilbert $C^*$-bimodules with two finite bases. We will construct a $C^*$-algebra from a Hilbert $C^*$-quad module of finite type and prove its universality subject to…

We give examples of minimal diffeomorphisms of compact connected manifolds which are not topologically orbit equivalent, but whose transformation group C*-algebras are isomorphic. The examples show that the following properties of a minimal…