发表机构
Università di Roma La Sapienza; University of Trieste; University of New South Wales（罗马第一大学; 的里雅斯特大学; 新南威尔士大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究由3维希尔伯特空间构造的最简单Motzkin子积系统，明确描述其Cuntz-Pimsner代数的谱仅含1维和2维不可约表示，并分析相关Thompson群与Cuntz代数的表示。
AI 中文摘要
Motzkin子积系统（SPS）由Motzkin代数的Jones-Wenzl幂等元构造而成，它推广了Temperley-Lieb SPS。最简单的Motzkin SPS（它不是Temperley-Lieb SPS）由一个3维希尔伯特空间构造。我们明确描述了相应的Cuntz-Pimsner代数的谱，该谱显著地仅允许维数为1和2的不可约表示，因此可被视为一个轻度量子空间。此外，我们还分析了与该谱相关联的Richard Thompson群和Cuntz代数的表示。
英文摘要
The Motzkin subproduct system (SPS) is constructed from the Jones Wenzl idempotents of the Motzkin algebras, which generalizes the Temperley Lieb SPS. The simplest Motzkin SPS, which is not a Temperley Lieb SPS, is constructed from a 3 dimensional Hilbert space. We explicitly describe the spectrum of the corresponding Cuntz Pimsner algebra, which remarkably admits only irreducible representations of dimensions 1 and 2, and can thus be viewed as a mildly quantum space. We moreover analyse representations of the Richard Thompson groups and of the Cuntz algebra that are associated to this spectrum.
CommentsAccepted for publication in International Journal of Mathematics
