Abstract

A correspondence over a C*-algebra $A$ is a right Hilbert $A$-module equipped with a nondegenerate left action of $A$ by adjointable operators. A correspondence may be viewed as an action of $\mathbb{N}$ by generalized endomorphisms of $A$. The analogue of a correspondence in the context of general semigroups is called aproduct system. In this talk I will consider Toeplitz algebras associated to product systems over group-embeddable monoids and discuss nuclearity for these algebras in relation to the coefficient algebra beyond the case of single correspondences and compactly aligned product systems over right LCM monoids.  We show that nuclearity of the Toeplitz algebra is equivalent tonuclearity of the coefficient algebra for every full product system of Hilbert bimodulesover abelian monoids and over Baumslag–Solitarmonoids. This is joint work with E. Katsoulis and M. Laca.