Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The dynamics of partial inverse semigroup actions   Given an inverse semigroup $S$ endowed with a partial action on a topological
space $X$, we construct a groupoid of germs $S\ltimes X$ in a manner similar to
Exel's groupoid of germs, and similarly a partial action of $S$ on an algebra
$A$ induces a crossed product $A\rtimes S$. We then prove, in the setting of
partial actions, that if $X$ is locally compact Hausdorff and zero-dimensional,
then the Steinberg algebra of the groupoid of germs $S\ltimes X$ is isomorphic
to the crossed product $A_R(X)\rtimes S$, where $A_R(X)$ is the Steinberg
algebra of $X$. We also prove that the converse holds, that is, that under
natural hypotheses, crossed products of the form $A_R(X)\rtimes S$ are
Steinberg algebras of appropriate groupoids of germs of the form $S\ltimes X$.
We introduce a new notion of topologically principal partial actions, which
correspond to topologically principal groupoids of germs, and study orbit
equivalence for these actions in terms of isomorphisms of the corresponding
groupoids of germs. This generalizes previous work of the first-named author as
well as from others, which dealt mostly with global actions of semigroups or
partial actions of groups. We finish the article by comparing our notion of
orbit equivalence of actions and orbit equivalence of graphs.

21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc