Lorentz and SU(3) groups derived from cubic quark algebra

TL;DR

This paper demonstrates that the Lorentz and SU(3) groups can be derived from a $Z_3$-graded cubic algebra structure associated with quarks, using a covariance principle that preserves a $Z_3$-graded three-form.

Contribution

It introduces a novel derivation of Lorentz and SU(3) groups from a $Z_3$-graded algebraic framework related to quarks, expanding the algebraic understanding of fundamental symmetries.

Findings

Lorentz and SU(3) groups derived from $Z_3$-graded algebra

Quark algebra with non-standard commutation laws

Covariance principle preserves $Z_3$-graded three-form

Abstract

We show that the Lorentz and the SU(3) groups can be derived from the covariance principle conserving a $Z_3$-graded three-form on a $Z_3$-graded cubic algebra representing quarks endowed with non-standard commutation laws.