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Wesley G. Lautenschlaeger

Publications and source records attributed to Wesley G. Lautenschlaeger.

10 recordsLinked to original sources
arXiv2026

An Ehresmann-Schein-Nambooripad-type theorem for left restriction semigroupoids

We introduce the concept of locally inductive constellations and establish isomorphisms between the categories of left restriction semigroupoids and locally inductive constellations. This construction offers an alternative to the celebrated Ehresmann-Schein-Nambooripad (ESN) Theorem and, in particular, generalizes results for one-sided restriction semigroups. We also obtain ESN-type theorems for one-sided restriction categories and inverse semigroupoids.

math.RA↗
arXiv2026

Groupoid Twisted Partial Actions

We introduce twisted partial actions of groupoids and establish necessary and sufficient conditions for the existence of a globalization. We prove that the crossed products associated with a twisted partial action and with its globalization are Morita equivalent. Finally, we extend partial projective representations and partial Schur multipliers to the groupoid setting and describe their interaction with twisted partial actions of groupoids.

math.RA↗
arXiv2026

The Szendrei Expansion of Restriction Semigroupoids

We introduce the concept of a restriction semigroupoid S, which unifies the notion of restriction semigroups and restriction categories within a single structure. We prove a representation theorem, showing that every restriction semigroupoid can be embedded into a determined category of partial maps. Furthermore, we construct the Szendrei expansion Sz(S) of S and establish that each premorphism between two restriction semigroupoids S and T is uniquely factorized by a morphism between the Szendrei expansion Sz(S) and T.

math.RA↗
arXiv2025

Galois Correspondence for Partial Groupoid Actions

We prove a Galois correspondence theorem for groupoids acting orthogonally and partially on commutative rings. We also consider partial actions that are not orthogonal, presenting two correspondences in this case: one for strongly Galois partial groupoid actions and one for global groupoid actions (without restriction). Some examples are presented.

math.RA↗
arXiv2025

Globalization of Partial Actions of Ordered Groupoids on Rings

We provide a necessary and sufficient condition to the existence of an ordered globalization of a partial ordered action of an ordered groupoid on a ring and we also present criteria to obtain uniqueness. Furthermore, we apply those results to obtain a Morita context and to show that an inverse semigroup partial action has a globalization (unique up to isomorphism) if, and only if, it is unital.

math.RA↗
arXiv2025

Galois Theory under inverse semigroup actions

We develop a Galois theory of commutative rings under actions of finite inverse semigroups. We present equivalences for the definition of Galois extension as well as a Galois correspondence theorem. We also show how the theory behaves in the case of inverse semigroups with zero.

math.RA↗
arXiv2023

Inverse Semigroupoid Actions and Representations

We show that there is a one-to-one correspondence between the partial actions of a groupoid $G$ on a set $X$ and the inverse semigroupoid actions of the Exel's inverse semigroupoid $S(G)$ on $X$. We also define inverse semigroupoid representations on a Hilbert space $H$, as well as the Exel's partial groupoid $C^*$-algebra $C_p^*(G)$, and we prove that there is a one-to-one correspondence between partial groupoid representations of $G$ on $H$, inverse semigroupoid representations of $S(G)$ on $H$ and $C^*$-algebra representations of $C_p^*(G)$ on $H$.

math.RA↗
arXiv2021

Galois Theory for Inverse Semigroup Orthogonal Actions

A Galois correspondence theorem is proved for the case of inverse semigroups acting orthogonally on commutative rings as a consequence of the Galois correspondence theorem for groupoid actions. To this end, we use a classic result of inverse semigroup theory that establishes a one-to-one correspondence between inverse semigroups and inductive groupoids.

math.RA↗