Weighted Cuntz algebras

Abstract

We study the C∗-algebra T/K where T is the C∗-algebra generated by d weighted shifts on the Fock space of Cd, F(Cd), (where the weights are given by a sequence {Zk} of matrices Zk∈Mdk(C)) and K is the algebra of compact operators on the Fock space. If Zk=I for every k, T/K is the Cuntz algebra Od. We show that T/K is isomorphic to a Cuntz--Pimsner algebra and use it to find conditions for the algebra to be simple. We present examples of simple and of nonsimple algebras of this type. We also describe the C∗-representations of T/K.