The Motzkin subproduct system

Abstract: We introduce a subproduct system of finite-dimensional Hilbert spaces using the Motzkin planar algebra and its 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.