Ternary symmetries and the Lorentz group
Volume 93 / 2011
Banach Center Publications 93 (2011), 51-58
MSC: Primary 20C35; Secondary 20C33, 81T75, 81T05, 08A02.
DOI: 10.4064/bc93-0-4
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. The ternary commutation relations on an algebra generated by two elements lead to cubic combinations of three quarks or antiquarks that transform as Lorentz spinors, and binary quark-anti-quark combinations that transform as Lorentz vectors.
