On q-tensor product of Cuntz algebras

2018/12/20 by Alexey Kuz'min, Alexey Kuzmin, Vasyl Ostrovskyi +6 · 1 citation
Mathematics · #46L05 (Primary) 46L35 #46L65 #46L80 #47A67 #81R10 (Secondary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.OA #math.QA #math.RT #msc:46L05 #msc:46L35 #msc:46L65 #msc:46L80 #msc:47A67 #msc:81R10

paper · pdf · doi:10.48550/arxiv.1812.08530

48 pages

openalex publication_date 2018/12/20 · arxiv created 2019/01/28 · arxiv updated 2019/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider C^*-algebra E_n,m^q, which is a q-twist of two Cuntz-Toeplitz algebras. For the case |q|<1 we give an explicit formula, which untwists the q-deformation, thus showing that the isomorphism class of E_n,m^q does not depend of q. For the case |q|=1 we give an explicit description of all ideals in E_n,m^q. In particular E_n,m^q contains unique largest ideal M_q. Then we identify E_n,m^q / M_q with the Rieffel deformation of O_n ⊗ O_m and use a K-theoretical argument to show that the isomorphism class does not depend on q.

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• On q-tensor products of Cuntz algebras

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