The Cuntz-Pimsner algebra of the simplest Motzkin subproduct system is 2-subhomogeneous

Source abstract

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. Moreover, we analyse representations of the Richard Thompson groups and of the Cuntz algebra that are associated to this spectrum.