Related papers: On certain Cuntz-Pimsner algebras

In this paper, we prove that if $\mathcal{A}$ is a unital separable $C^*$-algebra, $\mathcal{M}$ is a von Neumann algebra which has the Kirchberg's quotient weak expectation property (QWEP), and $\phi:\, \mathcal{A}\rightarrow \mathcal{M}$…

Suppose $A$ is a $C^*$-algebra and $H$ is a $C^*$-correspondence over $A$. If $H$ is regular in the sense that the left action of $A$ is faithful and is given by compact operators, then we compute the $K$-theory of $\mathcal{O}_A(H) \rtimes…

Combining the theory of extensions of C*-algebras and the Pimsner construction, we show that every countable infinite discrete group admits an ergodic action on arbitrary unital Kirchberg algebra. In the proof, we give a Pimsner…

In this paper we associate to every reduced C*-algebraic quantum group A a universal C*-algebraic quantum group. We fine tune a proof of Kirchberg to show that every *-representation of a modified L1-space is generated by a unitary…

Let $C$ be compact modular operator on a Hilbert C*-module $E$ satisfying property $\mathbb{[H]}$ [{\it J. Math. Phys.} {\bf 49} (2008), 033519], and let $ L :=I-C$. We prove the existence of a unique natural number $r$ for which $L^r$ is…

The homotopy symmetric $C^*$-algebras are those separable $C^*$-algebras for which one can unsuspend in E-theory. We find a new simple condition that characterizes homotopy symmetric nuclear $C^*$-algebras and use it to show that the…

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 define E-theory for separable C*-algebras over second countable topological spaces and establish its basic properties. This includes an approximation theorem that relates the E-theory over a general space to the E-theories over finite…

In this paper, we study multiplicative structures on the K-theory of the core $A:=C^*(E)^{U(1)}$ of the C*-algebra $C^*(E)$ of a directed graph $E$. In the first part of the paper, we study embeddings $E\to E\times E$ that induce a…

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,…

Algebras simple with respect to an action of Sweedler's algebra $H_4$ deliver the easiest example of $H$-module algebras that are $H$-simple but not necessarily semisimple. We describe finite dimensional $H_4$-simple algebras and prove the…

We construct an example of a simple approximately homogeneous C*-algebra such that its Elliott invariant admits an automorphism which is not induced by an automorphism of the algebra.

The universal C*-algebras of discrete product systems generalize the Toeplitz- Cuntz algebras and the Toeplitz algebras of discrete semigroups. We consider a semigroup P which is quasi-lattice ordered in the sense of Nica, and, for a…

Let A and B be $C^*$-algebras, A separable, and B $\sigma$-unital and stable. It is shown that there are natural isomorphisms $E(A,B)=KK(SA,Q(B))=[SA,Q(B)\otimes K]$, where $SA=C_0(0,1)\otimes A$, $[\cdot,\cdot]$ denotes the set of homotopy…

Algebras simple with respect to an action of a Taft algebra $H_{m^2}(\zeta)$ deliver an interesting example of $H$-module algebras that are $H$-simple but not necessarily semisimple. We describe finite dimensional $H_{m^2}(\zeta)$-simple…

A universal coefficient theorem is proved for C*-algebras over an arbitrary finite T_0-space X which have vanishing boundary maps. Under bootstrap assumptions, this leads to a complete classification of unital/stable real-rank-zero…

We show that a A-linear map of Hilbert A-modules is induced by a unitary Hilbert module operator if and only if it extends to an ordinary unitary on appropriately defined enveloping Hilbert spaces. Applications to the theory of…

Following Robert's [26], we study the structure of unitary groups and groups of approximately inner automorphisms of unital $C^*$-algebras, taking advantage of the former being Banach-Lie groups. For a given unital $C^*$-algebra $A$, we…

In this paper we show that the $\mathrm{K}$-homology groups of a separable C*-algebra can be enriched with additional descriptive set-theoretic information, and regarded as definable groups. Using a definable version of the Universal…

From a suitable groupoid G, we show how to construct an amenable principal groupoid whose C*-algebra is a Kirchberg algebra which is KK-equivalent to C*(G). Using this construction, we show by example that many UCT Kirchberg algebras can be…