WEIGHTED CUNTZ ALGEBRAS

We study the C*-algebra T/K where T is the C*-algebra generated by d weighted shifts on the Fock space of (Formula presented), F ((Formula presented)), (where the weights are given by a sequence {Zk} of matrices Zk (Formula presented) M_dt ((Formula presented))) and K is the algebra of compact operators on the Fock space. If Z_k = I for every k, T/ K is the Cuntz algebra O_d. 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.