In this paper, we show that every separable simple tracially approximately divisible C∗ C^*‐
algebra has strict comparison, and it is either purely infinite or has stable rank one. As a …

In this paper, we study almost finiteness and almost finiteness in measure of nonfree actions.
Let α: G↷ X α:G\curvearrowrightX be a minimal action of a locally finite‐by‐virtually ZZ group …

Given an algebraic action of a semigroup, we construct an inverse semigroup, and we
characterize Hausdorffness, topological freeness, and minimality of the associated tight …

We prove that a minimal second countable ample groupoid has dynamical comparison if
and only if its type semigroup is almost unperforated. Moreover, we investigate to what …

ON TRACIAL Z-STABILITY OF SIMPLE NON-UNITAL C∗-ALGEBRAS Introduction The Jiang-Su
algebra Z has become a cornerstone in the cl Page 1 ON TRACIAL Z-STABILITY OF SIMPLE …

Let G be a locally compact étale groupoid and L (L 2 (G)) be the C∗-algebra of adjointable
operators on the Hilbert C∗-module L 2 (G). In this paper, we discover a notion called quasi …

Given any quasi-countable, in particular, any countable inverse semigroup S, we introduce a
way to equip S with a proper and right subinvariant extended metric. This generalizes the …

We introduce the notion of (strong) subexponential growth for\'etale groupoids and study its
basic properties. In particular, we show that the K-groups of the associated groupoid $ L^ p …

We introduce the notion of dynamic asymptotic dimension growth for actions of discrete
groups on compact spaces, and more generally for locally compact\'etale groupoids with …

We construct Cartan subalgebras and hence groupoid models for classes of AH-algebras.
Our results cover all AH-algebras whose building blocks have base spaces of dimension at …