Ideal structure and pure infiniteness of ample groupoid C∗-algebras Page 1 Ergod. Th. &
Dynam. Sys. (2020), 40, 34–63 doi:10.1017/etds.2018.39 c Cambridge University Press, 2018 …

Amenability for groups can be extended to metric spaces, algebras over commutative fields
and C⁎-algebras by adapting the notion of Følner nets. In the present article we investigate …

We study representations of a Leavitt path algebra L of a finitely separated digraph Γ over a
field. We show that the category of L-modules is equivalent to a full subcategory of quiver …

We present a result of P. Ara which establishes that the Unbounded Generating Number
property is a Morita invariant for unital rings. Using this, we give necessary and sufficient …

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 …

In this paper, we introduce two new approximation properties for\'etale groupoids, almost
elementariness and (ubiquitous) fiberwise amenability, inspired by Matui's and Kerr's …

In this paper, we characterize when thep uniform Roe algebra of a metric space with
bounded geometry is (stably) finite and when it is properly infinite in standard form for p 2 …

We analyze the dichotomy amenable/paradoxical in the context of (discrete, countable,
unital) semigroups and corresponding semigroup rings. We consider also Følner type …

We introduce a notion of amenable normal extension S of a unital ring R with a finite
approximation system F, encompassing the amenable algebras over a field of Gromov and …

Given a discrete and countable inverse semigroup S one can study, in analogy to the group
case, its geometric aspects. In particular, we can equip S with a natural metric, given by the …