ИСТИНА

The complex D=4 Euclidean algebra and its real forms: Euclidian, Poincar\'{e} and Kleinian algebras and thir superextasions play a fundamental role in the relativistic physics - they are algebras of relativistic symmetries andsupersymmetries. Therefore it is very interesting to consider quantum deformations of these algebras.\\ Such quantum deformations are classified by classical r-matrices. In the case of the Poincar\'{e} algebra these r-matrices were classified already some time ago by S. Zakrzewski in ({\it Commun. Math. Phys.}, \textbf{187}, 285 (1997)) and their $N=1$ superextensions were presented in our paper (A.Borowiec, J.Lukierski and VNT: JHEP1206, 154 (2012)). A total list of twisted quantizations of the Zakrzewski results were obtained in (VNT: {\it Bulg.J.Phys.}, \textbf{35} (2008) 441--459).\\ In this talk I would like to present some results of a classification of the classical $r$-matrices for the complex $D=4$ Euclidean algebra and its real forms: Euclidean, Poincar\'{e} and Kleinian algebras and their N=1,2 superextensions. All these $r$-matrices generate the twisted quantum deformations which can be described in explicite form.\\ For this goal we use the following tools:\\ (1) graded structure of the $r$-matrices with respect to the four-momenta,\\ (2) notation of ''subordination'' for the classical $r$-matrices,\\ (3) algebraic structure of Cartan--Weyl bases of our (super)symmetries.