Related papers: Cartan subalgebras and the UCT problem

Building on recent work of Robertson and Steger, we associate a C*-algebra to a combinatorial object which may be thought of as a higher rank graph. This C*-algebra is shown to be isomorphic to that of the associated path groupoid.…

It is shown that, for an arbitrary free and minimal $\mathbb Z^n$-action on a compact Hausdorff space $X$, the crossed product C*-algebra $\mathrm{C}(X)\rtimes\mathbb Z^n$ always has stable rank one, i.e., invertible elements are dense.…

For unital $C^*$-algebras $A$ and $B$, we completely characterize the isometric ($*$-) automorphisms of their Banach space projective tensor product $A\otimes^\gamma B$. This leads to the characterization of inner and outer isometric…

In this paper, we investigate *-homomorphisms between C*-algebras associated to \'etale groupoids. First, we prove that such a *-homomorphism can be described by closed invariant subsets, groupoid homomorphisms and cocycles under some…

We calculate the Cuntz semigroup of the tensor product A with A. We restrict our attention to C*-algebras A which are unital, simple, nuclear, stably finite, have stable rank one, absorbs the Jiang-Su algebra tensorially and satisfy the…

In this note we state a conjecture that characterizes unital C*-algebras for which the unitary group is amenable as a topological group in the norm topology. We prove the conjecture for simple, separable, stably finite, unital, $\mathcal…

It has recently been proved that the class of unital exact C*-algebras is closed under taking reduced amalgamated free products. In particular, this implied that the class of exact discrete groups is closed under taking amalgamated free…

Let $(\mathcal{A}, G, \alpha)$ be a groupoid dynamical system. We show that if $G$ is assumed to be measurewise amenable and the section algebra $A = \Gamma_0(G^{(0)}, \mathcal{A})$ is nuclear, then the associated groupoid crossed product…

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 investigate Cartan subalgebras in nontracial amalgamated free product von Neumann algebras $M_1 \ast_B M_2$ over an amenable von Neumann subalgebra $B$. First, we settle the problem of the absence of Cartan subalgebra in arbitrary free…

von Neumann algebras have been playing an increasingly important role in the context of gauge theories and gravity. The crossed product presents a natural method for implementing constraints through the commutation theorem, rendering it a…

Let $P$ be a submonoid of a group $G$ and let $\mathcal{E}=(\mathcal{E}_p)_{p\in P}$ be a product system over $P$ with coefficient C*-algebra $A$. We show that the following C*-algebras are canonically isomorphic: the C*-envelope of the…

We prove the first rigidity and classification theorems for crossed product von Neumann algebras given by actions of non-discrete, locally compact groups. We prove that for arbitrary free probability measure preserving actions of connected…

We give a decomposition of the equivariant Kasparov category for discrete quantum group with torsions. As an outcome, we show that the crossed product by a discrete quantum group in a certain class preserves the UCT. We then show that…

Let $\mathcal{C}$ be a C*-algebra and $\alpha:\mathcal{C} \rightarrow \mathcal{C}$ a unital *-endomorphism. There is a natural way to construct operator algebras which are called semicrossed products, using a convolution induced by the…

We give a number of examples of exotic actions of locally compact groups on separable nuclear C*-algebras. In particular, we give examples of the following: (1) Minimal effective actions of ${\mathbb{Z}}$ and $F_n$ on unital nonsimple prime…

To every $C^*$ correspondence over a $C^*$-algebra one can associate a Cuntz-Pimsner algebra generalizing crossed product constructions, graph $C^*$-algebras, and a host of other classes of operator algebras. Cuntz-Pimsner algebras come…

We consider two twisted actions of a countable discrete group on $\sigma$-unital $C^*$-algebras. Then by taking the reduced crossed products, we get two inclusions of $C^*$-algebras. We suppose that they are strongly Morita equivalent as…

Let $A$ be a unital, simple and Z-stable C$^*$-algebra. We show that the set of positive elements in $A$ (resp. $A \otimes K$) belonging to a fixed non-compact Cuntz class is contractible as a topological subspace of $A$ (resp. $A \otimes…

We generalize the main result of Kamalov and show that if $G$ is an amenable discrete group with an action $\alpha$ on a finite nuclear unital $C^*$-algebra $A$ such that the reduced crossed product $A\rtimes_{\alpha,r} G$ has property $T$,…