Related papers: Non-semi-regular quantum groups coming from number…

We introduce the notion of continuous orbit equivalence for partial dynamical systems, and give an equivalent characterization in terms of Cartan-isomorphisms for partial C*-crossed products. Both graph C*-algebras and semigroup C*-algebras…

We characterize supramenable groups in terms of existence of invariant probability measures for partial actions on compact Hausdorff spaces and existence of tracial states on partial crossed products. These characterizations show that, in…

Motivated by work of Poguntke we study the question under what conditions simple subquotients of crossed products $A\rtimes_{\alpha}G$ by (twisted) actions of abelian groups $G$ are isomorphic to simple twisted group algebras of abelian…

We investigate approximation properties for $C^*$-algebras and their crossed products by actions and coactions by locally compact groups. We show that Haagerup's approximation constant is preserved for crossed products by arbitrary amenable…

Let $\sS$ be a countable, abelian semigroup of continuous surjections on a compact metric space $X$. Corresponding to this dynamical system we associate two operator algebras, the tensor algebra, and the semicrossed product. There is a…

We compare the algebras of the quantum automorphism group of finite-dimensional C$^\ast$-algebra $B$, which includes the quantum permutation group $S_N^+$, where $N = \dim B$. We show that matrix amplification and crossed products by…

A semigroupoid is a set equipped with a partially defined associative operation. Given a semigroupoid \Lambda we construct a C*-algebra C*(\Lambda) from it. We then present two main examples of semigroupoids, namely the Markov semigroupoid…

We study semigroup C*-algebras of semigroups associated with number fields and initial data arising naturally from class field theory. Using K-theoretic invariants, we investigate how much information about the initial number-theoretic data…

When S is a discrete subsemigroup of a discrete group G such that G = S^{-1} S, it is possible to extend circle-valued multipliers from S to G; to dilate (projective) isometric representations of S to (projective) unitary representations of…

We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…

We analyze existence of crossed product constructions of Lie group actions on C^*-algebras which are singular. These are actions where the group need not be locally compact, or the action need not be strongly continuous. In particular, we…

We compute the K-theory of a collection of C*-algebras, which we refer to as boundary C*-algebras, arising as the crossed product C*-algebras of lattice actions on the maximal Furstenberg boundaries of symmetric spaces of noncompact type.…

Let $K$ be a number field with ring of integers $R$. Given a modulus $\mathfrak{m}$ for $K$ and a group $\Gamma$ of residues modulo $\mathfrak{m}$, we consider the semi-direct product $R\rtimes R_{\mathfrak{m},\Gamma}$ obtained by…

We show that every topological k-graph constructed from a locally compact Hausdorff space {\Omega} and a family of pairwise commuting local homeomorphisms on {\Omega} satisfying a uniform boundedness condition on the cardinalities of…

The crossed products of locally C*-algebras are defined and a Takai duality theorem for inverse limit actions of a locally compact group on a locally C*-algebra is proved.

We study simplicity and pure infiniteness criteria for C*-algebras associated to inverse semigroup actions by Hilbert bimodules and to Fell bundles over etale not necessarily Hausdorff groupoids. Inspired by recent work of Exel and Pitts,…

We use compactifications of C*-algebras to introduce noncommutative coarse geometry. We transfer a noncommutative coarse structure on a C*-algebra with an action of a locally compact Abelian group by translations to Rieffel deformations and…

We prove uniqueness of representations of Nica-Toeplitz algebras associated to product systems of $C^*$-correspondences over right LCM semigroups by applying our previous abstract uniqueness results developed for $C^*$-precategories. Our…

Actions of locally compact groups and quantum groups on W*-ternary rings of operators are discussed and related crossed products introduced. The results generalise those for von Neumann algebraic actions with proofs based mostly on passing…

We introduce {\it covariant structures} $\left\{(\A,\k),(\a,\aa),\(\ha,\haa\)\right\}$ formed of a separable $C^*$-algebra $\A$, a measurable twisted action $(\a,\aa)$ of the second-countable locally compact group $\G$\,, a measurable…