The Poincaré algebras p(1,1) and p(1, 2): realizations and deformations

Abstract

All inequivalent realizations of the Poincaré algebras p(1,1) and p(1, 2) acting in spaces of not more than three variables are constructed. First-order deformations of p(1,1) and p(1,2) are proposed and the generic realizations for the initial and deformed Poincaré algebras are presented.