Eur. Phys. J. C (2008) 57: 601-611
https://doi.org/10.1140/epjc/s10052-008-0694-3

Regular Article - Theoretical Physics

Quantum deformations of D=4 Lorentz algebra revisited: twistings of q-deformation

¹ Institute for Theoretical Physics, University of Wrocław, pl. Maxa Borna 9, 50-205, Wrocław, Poland
² Institute of Nuclear Physics, Moscow State University, 119 992, Moscow, Russia
³ Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow region, 141980, Russia

^* e-mail: lukier@ift.uni.wroc.pl

Received: 29 April 2008
Revised: 24 June 2008
Published online: 26 August 2008

Abstract

This paper together with the previous one (Borowiec, Eur. Phys. J. C 48:633, 2006) presents a detailed description of all quantum deformations of the D=4 Lorentz algebra as a Hopf algebra in terms of complex and real generators. We describe here in detail two quantum deformations of the D=4 Lorentz algebra , obtained by twisting of the standard q-deformation . For the first twisted q-deformation an Abelian twist depending on the Cartan generators of is used. The second example of twisting provides a quantum deformation of Cremmer–Gervais type for the Lorentz algebra. For completeness we describe also twisting of the Lorentz algebra by a standard Jordanian twist. By twist quantization techniques we obtain for these deformations new explicit formulae for the deformed coproducts and antipodes of the -generators.