The Motzkin subproduct system

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${}^{\ast }$-algebras as universal C${}^{\ast }$-algebras, defined in terms of generators and relations, and we highlight properties of their representation theory.

Accepted for publication in International Journal of Mathematics