ИСТИНА

The Lorentz, Poincare and super-Poincare Lie algebras play a fundamental role in the relativistic physics - they are algebras of relativistic symmetries and supersymmetries. Therefore it is very interesting to consider quantum deformations of the algebras. These quantum deformations are clasified by classical r-matrices. There are two types of the classical r-matrices: standard and non-standard. The first type r-matrices satisfy the homogeneous classical Yang-Baxter equation (CYBE) and the second ones are solutions of the inhomogeneous (CYBE). In the case of the Lorentz algebra a complete list of the classical r-matrices involves the four independent formulas and the corresponding quantum deformations are presented in explicit form. In the case of Poincare algebra the total list of the non-standard classical r-matrices consists of 21 cases. These r-matrices have various numbers of free parameters and almost all of them can be presented as a sum of subordinated r-matrices of Abelian and Jordanian types. Almost all r-matrices of the list for the Poincare algebra can be extend to the Poincare superalgebra. Corresponding twists describing quantum deformations are given in explicit form.