Universal C*-algebras of endomorphisms of groups and partial actions

TL;DR

This paper introduces a novel approach to analyzing C*-algebras linked to injective endomorphisms of infinite cokernel groups, utilizing partial crossed product representations inspired by Boava and Exel's work.

Contribution

It develops a new framework for studying these C*-algebras through partial crossed products, offering insights without relying on traditional methods.

Findings

Constructs a partial crossed product representation of the C*-algebra.

Demonstrates properties of the algebra using partial action tools.

Provides a new perspective on endomorphism-related C*-algebras.

Abstract

We present a different way to study the C*-algebra associated with an injective endomorphism of a group G of infinite cokernel. We follow the work of Boava and Exel to construct a partial crossed product representation of that C*-algebra and show properties only using such tools.