On twist quantizations of D = 4 Lorentz and Poincare algebras

Abstract

We use the decomposition of o(3, 1) = sl(2; ℂ)1 ⊕sl(2; ℂ)2 in order to describe nonstandard quantum deformation of o(3, 1) linked with Jordanian deformation of sl(2; ℂ). Using the twist quantization technique, we obtain the deformed coproducts and antipodes, which can be expressed in terms of real physical Lorentz generators. We describe the extension of the considered deformation of D = 4 Lorentz algebra to the twist deformation of D = 4 Poincare algebra with dimensionless deformation parameter.