A construction of $C^*$-algebras from $C^*$-correspondences

TL;DR

This paper presents a new method for constructing $C^*$-algebras from $C^*$-correspondences, unifying several existing algebraic structures such as Cuntz-Pimsner algebras, crossed products, and graph algebras.

Contribution

It introduces a generalized construction framework that encompasses various known $C^*$-algebra classes derived from $C^*$-correspondences.

Findings

Unified construction method for $C^*$-algebras from correspondences

Generalizes Cuntz-Pimsner, crossed products, and graph algebras

Provides new tools for analyzing $C^*$-algebra structures

Abstract

We introduce a method to define $C^*$-algebras from $C^*$-correspondences. Our construction generalizes Cuntz-Pimsner algebras, crossed products by Hilbert $C^*$-modules, and graph algebras.