We prove two isomorphism-invariance theorems for groupoids associated with ultragraphs.
These theorems characterize ultragraphs for which the topological full group of an …

We study when the twisted groupoid Banach*-algebra L 1 (𝒢, σ) is Hermitian. In particular,
we prove that Hermitian groupoids satisfy the weak containment property. Furthermore, we …

We include a class of generalisations of Thompson's group $ V $ introduced by Melanie
Stein into the growing framework of topological full groups. Like $ V $, Stein's groups can be …

Inspired by a recent novel work of Good and Meddaugh, we establish fundamental
connections between shadowing, finite order shifts, and ultrametric complete spaces. We …

We study a class of generalisations of Thompson's group $ V $ arising naturally as
topological full groups of purely infinite, minimal groupoids. In the process, we show that the …

We extend ultragraph shift spaces and the realization of ultragraph C*-algebras as partial
crossed products to include ultragraphs with sinks (under a mild condition, called (RFUM2) …

We prove that Matui's AH conjecture holds for graph groupoids of infinite graphs. This is a
conjecture which relates the topological full group of an ample groupoid with the homology …

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 …

We define reduced and essential Banach algebras associated to a twisted\'{e} tale (not
necessarily Hausdorff) groupoid $(\mathcal {G},\mathcal {L}) $ and extend some …

Given an adaptable separated graph, we construct an associated groupoid and explore its
type semigroup. Specifically, we first attach to each adaptable separated graph a …