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H. Pinedo

Publications and source records attributed to H. Pinedo.

7 recordsLinked to original sources
arXiv2025

Twisted Steinberg algebras, regular inclusions and induction

Given a field $K$ and an ample (not necessarily Hausdorff) groupoid $G$, we define the concept of a line bundle over $G$ inspired by the well known concept from the theory of C*-algebras. If $E$ is such a line bundle, we construct the associated twisted Steinberg algebra in terms of sections of $E$, extending the original construction introduced independently by Steinberg in 2010, and by Clark, Farthing, Sims and Tomforde in a 2014 paper (originally announced in 2011). We also generalize (strictly, in the non-Hausdorff case) the 2023 construction of (cocycle) twisted Steinberg algebras of Armstrong, Clark, Courtney, Lin, Mccormick and Ramagge. We then extend Steinberg's theory of induction of modules, not only to the twisted case, but to the much more general case of regular inclusions of algebras. Among our main results, we show that, under appropriate conditions, every irreducible module is induced by an irreducible module over a certain abstractly defined isotropy algebra. We also describe a process of disintegration of modules and use it to prove a version of the Effros-Hahn conjecture, showing that every primitive ideal coincides with the annihilator of a module induced from isotropy.

math.OA↗
arXiv2023

Partial actions on quotient spaces and globalization

Given a partial action of a topological group $G$ on a space $X$, we determine properties $\mathcal P$ which can be extended from $X$ to its globalization. We treat the cases when $\mathcal P$ is any of the following: Hausdorff, regular, metrizable, second countable and having invariant metric. Further, for a normal subgroup $H$ we introduce and study a partial action of $G/H$ on the orbit space $X/\!\sim,$ applications to invariant metrics and inverse limits are presented.

math.GN↗
arXiv2018

Partial Groupoid Actions on Categories: Globalization and the smash product

In this article, we introduce the concept of partial groupoid actions on R- semicategories as well as we give criteria for existence of a globalization of it. This point of view is a generalization of the notions of partial groupoid actions on rings and partial group action on an R-semicategory. We also define the notions of partial skew groupoid category, smash product and describe functorial relations between them, in particular we show that the smash product is a Galois covering of its associated skew groupoid category.

math.RA↗