2010/09/20 by Nathan Brownlowe, Astrid an Huef, Brownlowe, Nathan +5
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.OA
paper · pdf · doi:10.48550/arxiv.1009.3678
arxiv created 2010/09/20 · openalex publication_date 2010/09/20 · arxiv updated 2010/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the Toeplitz algebra \TT(\N\rtimes\N^×) and three quotients of this algebra: the C^*-algebra \qn recntly introduced by Cuntz, and two new ones, which we call the additive and multiplicative boundary quotients. These quotients are universal for Nica-covariant representations of \N\rtimes\N^× satisfying extra relations, and can be realised as partial crossed products. We use the structure theory for partial crossed products to prove a uniqueness theorem for the additive boundary quotient, and use the recent analysis of KMS states on \TT(\nxnx) to describe the KMS states on the two quotients. We then show that \TT(\nxnx), \qn and our new quotients are all interesting new examples for Larsen's theory of Exel crossed products by semigroups.