Once again about quantum deformations of D=4 Lorentz algebra: twistings of q-deformation

Understand

This paper together with the previous one (arXiv:hep-th/0604146) presents the detailed description of all quantum deformations of D=4 Lorentz algebra as Hopf algebra in terms of complex and real generators.

• We describe here in detail two quantum deformations of the D=4 Lorentz algebra o(3,1) obtained by twisting of the standard q-deformation U_{q}(o(3,1)).
• For the first twisted q-deformation an Abelian twist depending on Cartan generators of o(3,1) is used.
• The second example of twisting provides a quantum deformation of Cremmer-Gervais type for the Lorentz algebra.