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arXiv · 2609.10349

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

Valeriano Aiello·Arnaud Brothier
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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. We moreover analyse representations of the Richard Thompson groups and of the Cuntz algebra that are associated to this spectrum.

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Valeriano Aiello, Arnaud Brothier. 2026-09-09. The Cuntz-Pimsner algebra of the simplest Motzkin subproduct system is 2-subhomogeneous. https://arxiv.org/abs/2609.10349

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