arXiv subjects

Paulinho Demeneghi

Publications and source records attributed to Paulinho Demeneghi.

3 recordsLinked to original sources

arXiv2025

A P-theorem for Inverse Semigroupoids through Ordered Globalizations

We prove that every ordered partial action of an inverse semigroupoid on a partially ordered set admits a globalization. This result is used to establish a connection between ordered partial actions of groupoids and a multi-object analogue of McAlister triples. As a consequence, we obtain a multi-object version of the P-theorem: every E-unitary inverse semigroupoid is isomorphic to a semidirect product arising from an ordered partial action of a groupoid on a multi-object version of a semilattice.

math.CT↗

arXiv2024

Globalization of partial inverse semigroupoid actions on sets

We prove that every partial action of an inverse semigroupoid on a set admits a universal globalization. Moreover, we show that our construction gives a reflector from the category of partial actions on the full subcategory of global actions. Finally, we investigate if the mediating function given by the universal property of our construction is injective.

math.OA↗

arXiv2018

The Ideal Structure of Steinberg Algebras

Given an ample action of an inverse semigroup on a locally compact and Hausdorff topological space, we study the ideal structure of the crossed product algebra associated with it. By developing a theory of induced ideals, we manage to prove that every ideal in the crossed product algebra may be obtained as the intersection of ideals induced from isotropy group algebras. This can be interpreted as an algebraic version of the Effros-Hahn conjecture. Finally, as an application of our result, we study the ideal structure of a Steinberg algebra associated with an ample groupoid by interpreting it as an inverse semigroup crossed product algebra.

math.OA↗