Partial Crossed Product of a group G vs Crossed Product of S(G)

TL;DR

This paper introduces a new definition for partial crossed products by inverse semigroup actions on C*-algebras, and establishes an isomorphism with partial crossed products by group actions, expanding the theoretical framework.

Contribution

It proposes a novel definition of partial crossed products without covariant representations and proves an isomorphism with crossed products by inverse semigroup actions.

Findings

New definition of partial crossed product without covariant representations

Isomorphism between partial crossed products of group G and inverse semigroup S(G)

Enhanced understanding of the structure of partial crossed products

Abstract

In this work we present a new definition to the Partial Crossed Product by actions of inverse semigroups in a C^*-algebra, without using the covariant representations as Sieben did in [5]. Also we present an isomorphism between the partial crossed products by partial actions of a group G and the partial crossed product by actions of S(G), an inverse semigroup associated to G introduced by Exel in [2].