ИСТИНА

Using the isomorphism o(3;C)  sl(2;C) we develop a new simple algebraic technique for complete classification of quantum deformations (the classical r-matrices) for real forms o(3) and o(2, 1) of the complex Lie algebra o(3;C) in terms of real forms of sl(2;C): su(2), su(1, 1) and sl(2;R). We prove that the D = 3 Lorentz symmetry o(2, 1)  su(1, 1)  sl(2;R) has three different Hopfalgebraic quantum deformations, which are expressed in the simplest way by two standard su(1, 1) and sl(2;R) qanalogs and by simple Jordanian sl(2;R) twist deformation. These quantizations are presented in terms of the quantum Cartan–Weyl generators for the quantized algebras su(1, 1) and sl(2;R) as well as in terms of quantum Cartesian generators for the quantized algebra o(2, 1). Finally, some applications of the deformed D = 3 Lorentz symmetry are mentioned.