Related papers: C*-algebras associated with integral domains and c…

We realize Kellendonk'?s C*-algebra of an aperiodic tiling as the tight C*-algebra of the inverse semigroup associated to the tiling, thus providing further evidence that the tight C*-algebra is a good candidate to be the natural…

In this paper we suggest a definition for a C*-algebra attached to an injective morphism of some \'Etale groupoid. We take into account all the peculiarities of such objects and present some interesting relations with already well-known…

We classify extensions of certain classifiable C*-algebras using the six term exact sequence in K-theory together with the positive cone of the K_0-groups of the distinguished ideal and quotient. We then apply our results to a class of…

We compute the $K$-theory of crossed products of rotation algebras $\mathcal{A}_\theta$, for any real angle $\theta$, by matrices in $\mathrm{SL}(2,\mathbb{Z})$ with infinite order. Using techniques of continuous fields, we show that the…

We introduce algebraic dynamical systems, which consist of an action of a right LCM semigroup by injective endomorphisms of a group. To each algebraic dynamical system we associate a C*-algebra and describe it as a semigroup C*-algebra. As…

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,…

Partial actions of discrete abelian groups can be used to construct both groupoid C*-algebras and partial crossed product algebras. In each case there is a natural notion of an analytic subalgebra. We show that for countable subgroups of…

We study the space of irreducible representations of a crossed product C*-algebra AxG, where G is a finite group. We construct a space $\Gamma$ which consists of pairs of irreducible representations of A and irreducible projective…

To a domain with conical points \Omega, we associate a natural C*-algebra that is motivated by the study of boundary value problems on \Omega, especially using the method of layer potentials. In two dimensions, we allow \Omega to be a…

We study $C^*$-algebras arising from $C^*$-correspondences, which was introduced by the author. We prove the gauge-invariant uniqueness theorem, and obtain conditions for our $C^*$-algebras to be nuclear, exact, or satisfy the Universal…

We provide some background on the category of classifiable $\mathrm{C}^*$-algebras, whose objects are infinite-dimensional, simple, separable, unital $\mathrm{C}^*$-algebras that have finite nuclear dimension and satisfy the universal…

We continue the study of the effective content of $K$-theory for C*-algebras, with a focus on AF algebras. We show that from a c.e. presentation of an AF algebra it is possible to compute a representation of the algebra as an inductive…

We give an explicit injective representation of the universal $\mathrm{C}^\ast$-algebra that is generated by doubly non-commuting isometries. This injectivity allows us to prove that such universal algebras embed naturally into each other…

Using Kirchberg-Phillips' classification of purely infinite C*-algebras by K-theory, we prove that the isomorphism types of crossed product C*-algebras associated to certain hyperbolic 3-manifold groups acting on their Gromov boundary only…

We define a broad class of crossed product C*-algebras of the form C(G)xG, where G is a discrete countable amenable residually finite group, and G is a profinite completion of G. We show that they are unital separable simple nuclear…

Let $\Gamma$ be a discrete group. To every ideal in $\ell^{\infty}(\G)$ we associate a C$^*$-algebra completion of the group ring that encapsulates the unitary representations with matrix coefficients belonging to the ideal. The general…

For an action of a finite group on a C*-algebra, we present some conditions under which properties of the C*-algebra pass to the crossed product or the fixed point algebra. We mostly consider the ideal property, the projection property,…

We introduce the notion of a crossed product of an algebra by a coalgebra $C$, which generalises the notion of a crossed product by a bialgebra well-studied in the theory of Hopf algebras. The result of such a crossed product is an algebra…

We show that unital simple C*-algebras with tracial topological rank zero which are locally approximated by subhomogeneous C^-algebras can be classified by their ordered $K$-theory. We apply this classification result to show that certain…

We introduce a new class of C^*-algebras, which is a generalization of both graph algebras and homeomorphism C^*-algebras. This class is very large and also very tractable. We prove the so-called gauge-invariant uniqueness theorem and the…