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arXiv · 2502.14057

The Motzkin subproduct system

Valeriano Aiello·Simone Del Vecchio·Stefano Rossi
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Abstract

We introduce a subproduct system of finite-dimensional Hilbert spaces by using the Motzkin planar algebra and its Motzkin Jones-Wenzl idempotents, which generalizes the Temperley-Lieb subproduct system of Habbestad and Neshveyev. We provide a description of the corresponding Toeplitz and Cuntz-Pimsner C$^*$-algebras as universal C$^*$-algebras, defined in terms of generators and relations, and we highlight properties of their representation theory.

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Valeriano Aiello, Simone Del Vecchio, Stefano Rossi. 2025-02-19. The Motzkin subproduct system. https://doi.org/10.1142/s0129167x25500600

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