The Motzkin subproduct system
Operator Algebras
2025-11-18 v3 Quantum Algebra
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.
Cite
@article{arxiv.2502.14057,
title = {The Motzkin subproduct system},
author = {Valeriano Aiello and Simone Del Vecchio and Stefano Rossi},
journal= {arXiv preprint arXiv:2502.14057},
year = {2025}
}
Comments
Accepted for publication in International Journal of Mathematics