The Motzkin sub-product system

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[Formula: see text]-algebras as universal C[Formula: see text]-algebras, defined in terms of generators and relations, and we highlight properties of their representation theory.