Related papers: C^*-algebras from k group representations

Let $G$ be a locally compact group with cocompact connected component. We prove that the assembly map from the topological $\k$-theory of $G$ to the $\k$-theory of the reduced $C^*$-algebra of $G$ is an isomorphism.

We introduce the notion of locally finite decomposition rank, a structural property shared by many stably finite nuclear C*-algebras. The concept is particularly relevant for Elliott's program to classify nuclear C*-algebras by K-theory…

We prove a uniqueness theorem and give a characterization of simplicity for Steinberg algebras associated to non-Hausdorff ample groupoids. We also prove a uniqueness theorem and give a characterization of simplicity for the C*-algebra…

We give an example of a simple separable C*-algebra which is not isomorphic to its opposite algebra. Our example is nonnuclear and stably finite, has real rank zero and stable rank one, and has a unique tracial state. It has trivial K_1,…

We present and study C*-algebras generated by "periodic weighted creation operators" on the Fock space associated with an automorphism $\alpha$ on a C*-algebra $A$. These algebras can be viewed as generalized Bunce-Deddens algebras…

We consider two Z/2Z-actions on the Podles generic quantum spheres. They yield, as noncommutative quotient spaces, the Klimek-Lesniewski q-disc and the quantum real projective space, respectively. The C*-algebras of all these quantum spaces…

Let $G$ be the linear algebraic group $SL_3$ over a field $k$ of characteristic two. Let $A$ be a finitely generated commutative $k$-algebra on which $G$ acts rationally by $k$-algebra automorphisms. We show that the full cohomology ring…

We consider the boundary-path groupoids of topological higher-rank graphs. We show that the all such groupoids are topologically amenable. We deduce that the C*-algebras of topological higher-rank graphs are nuclear and prove versions of…

We describe a class of $C^*$-algebras which simultaneously generalise the ultragraph algebras of Tomforde and the shift space $C^*$-algebras of Matsumoto. In doing so we shed some new light on the different $C^*$-algebras that may be…

We give a classification theorem for unital separable simple nuclear $C^*$-algebras with tracial topological rank zero which satisfy the Universal Coefficient Theorem. We prove that if $A$ and $B$ are two such $C^*$-algebras and $$ (K_0(A),…

In this paper, two sufficient and necessary conditions are given. The first one characterizes when the boundary path groupoid of a topological graph without singular vertices has closed interior of its isotropy group bundle, and the second…

We consider a construction of C*-algebras from continuous piecewise monotone maps on the circle which generalizes the crossed product construction for homeomorphisms and more generally the construction of Renault, Deaconu and…

We consider a class of C*-algebras associated to one parameter continuous tensor product systems of Hilbert modules, which can be viewed as continuous counterparts of Pimsner's Toeplitz algebras. By exhibiting a homotopy of…

In this paper we study the C*-envelope of the (non-self-adjoint) tensor algebra associated via subproduct systems to a finite irreducible stochastic matrix $P$. Firstly, we identify the boundary representations of the tensor algebra inside…

Given a connected and locally compact Hausdorff space X with a good base K we assign, in a functorial way, a C(X)-algebra to any precosheaf of C*-algebras A defined over K. Afterwards we consider the representation theory and the Kasparov…

Given a graph of C*-algebras, we prove a long exact sequence in KK-theory for both the maximal and the vertex-reduced fundamental C*-algebras in the presence of possibly non GNS-faithful conditional expectations. We deduce from it the…

In a previous paper we prove that any semisimple triangular Hopf algebra A over an algebraically closed field of characteristic 0 (say the field of complex numbers C) is obtained from a finite group after twisting the ordinary…

Suppose that A is a separable C*-algebra and that G_* is a (graded) subgroup of K_*(A). Then there is a natural short exact sequence 0 \to G_* \to K_*(A) \to K_*(A)/G_* \to 0. In this note we demonstrate how to geometrically realize this…

We generalize the Li-Yang notion of self-similar $k$-graph $(G,\Lambda)$ and its $C^*$-algebra $\mathcal{O}_{G,\Lambda}$ to any finitely aligned $k$-graph $\Lambda$. We then introduce an inverse semigroup model for $\mathcal{O}_{G,\Lambda}$…

We introduce an algebraic version of the Katsura $C^*$-algebra of a pair $A,B$ of integer matrices and an algebraic version of the Exel-Pardo $C^*$-algebra of a self-similar action on a graph. We prove a Graded Uniqueness Theorem for such…