We introduce a sub-product system of finite-dimensional Hilbert spaces by using the Motzkin planar algebra and its Motzkin Jones–Wenzl idempotents, which generalizes the Temperley–Lieb sub-product 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.
The Motzkin sub-product system / Aiello, Valeriano; Del Vecchio, Simone; Rossi, Stefano. - In: INTERNATIONAL JOURNAL OF MATHEMATICS. - ISSN 0129-167X. - 36:14(2025), pp. 1-37. [10.1142/S0129167X25500600]
The Motzkin sub-product system
Valeriano Aiello
;
2025
Abstract
We introduce a sub-product system of finite-dimensional Hilbert spaces by using the Motzkin planar algebra and its Motzkin Jones–Wenzl idempotents, which generalizes the Temperley–Lieb sub-product 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.| File | Dimensione | Formato | |
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