Groupoid Twisted Partial Actions

TL;DR

This paper introduces twisted partial actions of groupoids, generalizes the globalization theorem, and explores their Morita equivalence and connections to partial projective representations and Schur multipliers.

Contribution

It extends the theory of partial actions to groupoids, providing new results on globalization, Morita equivalence, and partial projective representations.

Findings

Existence of an enveloping (globalization) action for twisted partial groupoid actions

Morita equivalence between crossed products of twisted partial and global actions

Generalization of partial projective representations and Schur multipliers for groupoids

Abstract

The main goal of this paper is to introduce the notion of twisted partial action of groupoids. We generalize the theorem about the existence of an enveloping action, also known as the globalization theorem, and show that the crossed products of the twisted partial action and of its associated twisted global action are Morita equivalent. Finally, we generalize the concepts of partial projective representation and partial Schur multiplier for a groupoid, and we show the interaction between groupoid partial projective representions and groupoid twisted partial actions.