C*-algebras for partial product systems over $\mathbb{N}$

Abstract: We define partial product systems over \mathbb{N}. They generalise product systems over $\mathbb{N}$ and Fell bundles over $\mathbb{Z}$. We define Toeplitz C∗-algebras and relative Cuntz–Pimsner algebras for them and show that the section C∗-algebra of a Fell bundle over $\mathbb{Z}$ is a relative Cuntz–Pimsner algebra. We describe the gauge-invariant ideals in the Toeplitz C∗-algebra.