2020/06/18 by Leonid Helmer, Helmer, Leonid, Baruch Solel +1
Mathematics · #46L05 #46L08 #46L35 #46L89 #47L80 #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2006.10372
openalex publication_date 2020/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 non simple algebras of this type. We also describe the C^*-representations of T/K.