The Motzkin subproduct system

TL;DR

This paper introduces a new subproduct system based on the Motzkin planar algebra, generalizing existing systems, and characterizes its associated Toeplitz and Cuntz-Pimsner C*-algebras through generators, relations, and representation theory.

Contribution

It presents the construction of a Motzkin subproduct system and describes its Toeplitz and Cuntz-Pimsner C*-algebras as universal algebras with detailed representation properties.

Findings

Defined a new subproduct system using Motzkin planar algebra.

Characterized the associated Toeplitz and Cuntz-Pimsner C*-algebras.

Analyzed the representation theory of these algebras.

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.