Title: The interplay between Steinberg algebras and partial skew rings,
Abstract: We study the interplay between Steinberg algebras and partial skew rings: For
a partial action of a group in a Hausdorff, locally compact, totally
disconnected topological space, we realize the associated partial skew group
ring as a Steinberg algebra (over the transformation groupoid attached to the
partial action). We then apply this realization to characterize diagonal
preserving isomorphisms of partial skew group rings, over commutative algebras,
in terms of continuous orbit equivalence of the associated partial actions.
Finally, we show that any Steinberg algebra, associated to a Hausdorff ample
groupoid, can be seen as a partial skew inverse semigroup ring.