Partial group algebra with projections and relations

TL;DR

This paper introduces a new class of C*-algebras called partial group algebras with projections and relations, demonstrating their structure as partial crossed products and connecting them to known algebras like Cuntz-Krieger and graph algebras.

Contribution

It defines partial group algebras with projections and relations and shows they can be realized as partial crossed products, linking them to existing C*-algebra frameworks.

Findings

Partial group algebras with projections and relations are partial crossed products.

Examples include Cuntz-Krieger algebras and unitizations of graph C*-algebras.

The structure unifies various known C*-algebras under a common framework.

Abstract

We introduce the notion of the partial group algebra with projections and relations and show that this C*-algebra is a partial crossed product. Examples of partial group algebras with projections and relations are the Cuntz-Krieger algebras and the unitization of C*-algebras of directed graphs.