C*-Algebras for partial product systems over N

TL;DR

This paper introduces partial product systems over N, generalizing existing structures, and develops associated Toeplitz and Cuntz-Pimsner C*-algebras, linking them to Fell bundles over Z and analyzing their ideal structure.

Contribution

It defines partial product systems over N and constructs their Toeplitz and Cuntz-Pimsner algebras, extending the theory of product systems and Fell bundles.

Findings

Section C*-algebra of a Fell bundle over Z is a relative Cuntz-Pimsner algebra.

Characterization of gauge-invariant ideals in Toeplitz C*-algebra.

Generalization of product systems and Fell bundles over N and Z.

Abstract

We define partial product systems over N. They generalise product systems over N and Fell bundles over Z. We define Toeplitz C*-algebras and relative Cuntz-Pimsner algebras for them and show that the section C*-algebra of a Fell bundle over Z is a relative Cuntz-Pimsner algebra. We describe the gauge-invariant ideals in the Toeplitz C*-algebra.