Morita Equivalence of C^*-Crossed Products by Inverse Semigroup Actions and Partial Actions

TL;DR

This paper introduces Morita equivalence concepts for twisted inverse semigroup actions and partial actions, establishing that Morita equivalent actions lead to Morita equivalent crossed products, thus linking algebraic structures and their representations.

Contribution

It defines Morita equivalence for twisted inverse semigroup actions and partial actions, and proves the equivalence of their crossed products, advancing the understanding of their algebraic relationships.

Findings

Morita equivalence of actions implies Morita equivalence of crossed products

Introduces Morita equivalence for twisted inverse semigroup actions

Establishes a connection between algebraic actions and their crossed products

Abstract

Morita equivalence of twisted inverse semigroup actions and discrete twisted partial actions are introduced. Morita equivalent actions have Morita equivalent crossed products.