Related papers: Hereditary uniform property $\Gamma$

In this paper, let $A$ be a unital separable simple infinite dimensional C*-algebra which has uniform property $\Gamma$. Let $\alpha\colon G\to \mathrm{Aut}(A)$ be an action of a finite group which has the weak tracial Rokhlin property.…

We give an example of an exact, stably finite, simple. separable C*-algebra D which is not isomorphic to its opposite algebra. Moreover, D has the following additional properties. It is stably finite, approximately divisible, has real rank…

We revisit the notion of tracial approximation for unital simple C*-algebras. We show that a unital simple separable C*-algebra A is asymptotically tracially in the class of C*-algebras with finite nuclear dimension if and only if A is…

In this article, we study the permanence of topological and algebraic dimension type properties of simple unital $C\sp*$-algebras. When a pair of unital $C\sp*$-algebras $(A, B)$ is associated by a $*$-homomorphism $\phi: A\to B$ which is…

We introduce a notion of a uniform structure on the set of all representations of a given separable, not necessarilly commutative $C^*$-algebra $\mathfrak{A}$ by introducing a suitable family of metrics on the set of representations of…

Suppose that A is a C*-algebra for which A is isomorphic to A tensor Z, where Z is the Jiang-Su algebra: a unital, simple, stably finite, separable, nuclear, infinite dimensional C*-algebra with the same Elliott invariant as the complex…

We investigate the tracial and ideal structures of $C^*$-algebras of quasi-regular representations of stabilizers of boundary actions. Our main tool is the notion of boundary maps, namely $\Gamma$-equivariant unital completely positive maps…

We prove that a graph C*-algebra with exactly one proper nontrivial ideal is classified up to stable isomorphism by its associated six-term exact sequence in K-theory. We prove that a similar classification also holds for a graph C*-algebra…

We show that the following properties of the C*-algebras in a class $\mathcal{P}$ are inherited by simple unital ${\rm C^*}$-algebras in the class of asymptotically tracially in $\mathcal{P}$: $(1)$ $\beta$-comparison (in the sense of…

Let Z denote the simple limit of prime dimension drop algebras that has a unique tracial state. Let A != 0 be a unital C^*-algebra with A = A tensor Z. Then the homotopy groups of the group U(A) of unitaries in A are stable invariants,…

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.…

We show that the following divisible properties of the ${\rm C^*}$-algebras in a class $\mathcal{P}$ are inherited by simple unital ${\rm C^*}$-algebras in the class of asymptotically tracially in $\mathcal{P}$: $(1)$ $m$-almost divisible,…

Let $\Gamma$ be a countable discrete group. We say that $\Gamma$ has $C^*$-invariant subalgebra rigidity (ISR) property if every $\Gamma$-invariant $C^*$-subalgebra $\mathcal{A}\le C_r^*(\Gamma)$ is of the form $C_r^*(N)$ for some normal…

We investigate the notion of tracial $\mathcal Z$-stability beyond unital C*-algebras, and we prove that this notion is equivalent to $\mathcal Z$-stability in the class of separable simple nuclear C*-algebras.

It is shown that a unital C*-algebra A has the Dixmier property if and only if it is weakly central and satisfies certain tracial conditions. This generalises the Haagerup-Zsido theorem for simple C*-algebras. We also study a uniform…

A discrete group $\Gamma$ is C*-simple if the C*-algebra $C_\lambda^*(\Gamma)$ generated by the range of the left regular representation $\lambda$ on $\ell^2(\Gamma)$ is simple. In this case, $\Gamma$ acts faithfully on the Furstenberg…

Let $A$ be a separable, unital, simple C*-algebra with stable rank one. We show that every strictly positive, lower semicontinuous, affine function on the simplex of normalized quasitraces of $A$ is realized as the rank of an operator in…

We introduce diagonal comparison, a regularity property of diagonal pairs where the sub-C*-algebra has totally disconnected spectrum, and establish its equivalence with the concurrence of strict comparison of the ambient C*-algebra and…

A classification is given of certain separable nuclear C*-algebras not necessarily of real rank zero, namely the class of simple C*-algebras which are inductive limits of continuous-trace C*-algebras whose building blocks have their…

We demonstrate that pure C*-algebras form a robust class by proving that pureness follows from very weak comparison and divisibility properties. Using this, we show that every simple, non-elementary C*-algebra with a unique quasitrace and…