We investigate Cuntz-Pimsner C∗-algebras associated with certain correspondences of the unit circle T. We analyze these C∗-algebras by analogy with irrational rotation algebras Aθ and Cuntz algebras On. We construct a Rieffel type projection, study the fixed point algebras of certain actions of finite groups, and calculate the entropy of a certain endomorphism. We also study the induced map of ...

A semigroupoid is a set equipped with a partially defined associative operation. Given a semigroupoid Λ we construct a C*-algebra O(Λ) from it. We then present two main examples of semigroupoids, namely the Markov semigroupoid associated to an infinite 0–1 matrix, and the semigroupoid associated to a higher-rank graph. In both cases the semigroupoid C*-algebra is shown to be isomorphic to the a...

Given an ultragraph in the sense of Tomforde, we construct a topological quiver in the sense of Muhly and Tomforde in such a way that the universal C∗-algebras associated to the two objects coincide. We apply results of Muhly and Tomforde for topological quiver algebras and of Katsura for topological graph C∗-algebras to study the K-theory and gauge-invariant ideal structure of ultragraph C∗-al...

Let ζ and η be distinct points on the unit circle and suppose that φ is a linear-fractional self-map of the unit disk D, not an automorphism, with φ(ζ) = η. We describe the C-algebra generated by the associated composition operator Cφ and the shift operator, acting on the Hardy space on D.

We give a detailed survey of the theory of quasidiagonal C∗-algebras. The main structural results are presented and various functorial questions around quasidiagonality are discussed. In particular we look at what is currently known (and not known) about tensor products, quotients, extensions, free products, etc. of quasidiagonal C∗-algebras. We also point out how quasidiagonality is connected ...