Globalization of twisted partial actions

TL;DR

This paper investigates conditions under which a twisted partial group action on a unital ring can be extended to a global action, establishing criteria for existence, uniqueness, and Morita equivalence of the associated crossed products.

Contribution

It provides new criteria for the existence and uniqueness of globalizations of twisted partial actions on unital rings, linking them to multiplier extendibility.

Findings

Criteria for the existence of globalization of twisted partial actions.

Uniqueness of globalization up to a certain equivalence.

Morita equivalence between crossed products of partial and global actions.

Abstract

Let A be a unital ring which is a product of possibly infinitely many indecomposable rings. We establish criteria for the existence of a globalization for a given twisted partial action of a group on A. If the globalization exists, it is unique up to a certain equivalence relation and, moreover, the crossed product corresponding to the twisted partial action is Morita equivalent to that corresponding to its globalization. For arbitrary unital rings the globalization problem is reduced to an extendibility property of the multipliers involved in the twisted partial action.