Matrix equations and trilinear commutation relations

TL;DR

This paper explores an algebraic framework for matrix models with mass terms, linking equations of motion to trilinear commutation relations and constructing noncommutative spheres, highlighting their equivalence to parafermions.

Contribution

It introduces a novel algebraic approach connecting matrix equations to trilinear relations and demonstrates the construction of noncommutative spheres within this framework.

Findings

Established a connection between matrix equations and trilinear commutation relations.

Constructed explicit solutions including noncommutative spheres.

Showed the equivalence of fuzzy spheres and parafermions.

Abstract

In this paper we discuss a general algebraic approach to treating static equations of matrix models with a mass-like term. In this approach the equations of motions are considered as consequence of parafermi-like trilinear commutation relations. In this context we consider several solutions, including construction of noncommutative spheres. The equivalence of fuzzy spheres and parafermions is underlined.