Description of Partial actions

TL;DR

This paper investigates partial group actions on algebras over a commutative ring, providing descriptions for indecomposable cases and extending to decomposable algebras via global actions.

Contribution

It offers a detailed characterization of partial group actions on indecomposable and decomposable algebras, linking partial and global actions in these contexts.

Findings

Description of partial actions on indecomposable algebras

Extension of partial actions to decomposable algebras

Representation of partial actions via global actions

Abstract

In this paper, we study partial actions of groups on $R$-algebras, where $R$ is a commutative ring. We describe the partial actions of groups on the indecomposable algebras with enveloping actions. Then we work on algebras that can be decomposed as product of indecomposable algebras and we give a description of the partial actions of groups on these algebras in terms of global actions.