We study the category of left unital graded modules over the Steinberg algebra of a graded
ample Hausdorff groupoid. In the first part of the paper, we show that this category is …

When the theory of Leavitt path algebras was already quite advanced, it was discovered that
some of the more difficult questions were susceptible to a new approach using topological …

We study Steinberg algebras constructed from ample Hausdorff groupoids over commutative
integral domains with identity. We reconstruct (graded) groupoids from (graded) Steinberg …

We study strongly graded groupoids, which are topological groupoids G equipped with a
continuous, surjective functor κ: G→ Γ, to a discrete group Γ, such that κ− 1 (γ) κ− 1 (δ)= κ− 1 …

We consider the ideal structure of Steinberg algebras over a commutative ring with identity.
We focus on Hausdorff groupoids that are strongly effective in the sense that their reductions …

We introduce twisted Steinberg algebras over a commutative unital ring R. These generalise
Steinberg algebras and are a purely algebraic analogue of Renault's twisted groupoid C …

Given a graded ample Hausdorff groupoid, we realise its graded Steinberg algebra as a
partial skew inverse semigroup ring. We use this to show that for a partial action of a discrete …

Given a row-finite higher-rank $ k $-graph $\Lambda $, we define a commutative monoid $
T_\Lambda $ which is a higher-rank analogue of the talented monoid of a directed graph …

We prove the Effros-Hahn conjecture for groupoid algebras with coefficients in a sheaf,
obtaining as a consequence a description of the ideals in skew inverse semigroup rings. We …

We give a one-to-one correspondence between ideals in the Steinberg algebra of a
Hausdorff ample groupoid G, and certain families of ideals in the group algebras of isotropy …