V. N. Tolstoy

Jordanian twist quantization of D = 4 Lorentz and Poincaré algebras and D = 3 contraction limit

We describe in detail the two-parameter nonstandard quantum deformation of the D=4 Lorentz algebra

N = \frac{1}{2} deformations of chiral superspaces from new quantum Poincaré and Euclidean superalgebras

\mathfrak{o}(3,1)

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

, linked with a Jordanian deformation of

Projection Operator Method for Quantum Groups

\mathfrak{sl}(2;\mathbb{C})

On twist quantizations of D = 4 Lorentz and Poincare algebras

. Using the twist quantization technique we obtain the explicit formulae for the deformed co-products and antipodes. Further extending the considered deformation to the D=4 Poincaré algebra we obtain a new Hopf-algebraic deformation of four-dimensional relativistic symmetries with a dimensionless deformation parameter. Finally, we interpret

Quantum deformations of D = 4 Euclidean, Lorentz, Kleinian and quaternionic o⋆(4) symmetries in unified o(4;C) setting

\mathfrak{o}(3,1)

New approach in theory of Clebsch-Gordan coefficients foru(n) andU q(u(n))

as the D=3 de Sitter algebra and calculate the contraction limit

Multiparameter Quantum Deformations of Jordanian Type for Lie Superalgebras

R\rightarrow\infty

Basic twist quantization of the exceptional Lie algebra g2

(R is the de Sitter radius) providing an explicit Hopf algebra structure for the quantum deformation of the D=3 Poincaré algebra (with mass-like deformation parameters), which is the two-parameter light-cone κ-deformation of the D=3 Poincaré symmetry.

q-Weyl coefficients forU q (3) andq-Racah coefficients forSU q (2)

A bstractWe present a large class of supersymmetric classical r-matrices, describing the supertwist deformations of Poincaré and Euclidean superalgebras. We consider in detail new family of four supertwists of N = 1 Poincaré superalgebra and provide as well their Euclidean counterpart. The proposed supertwists are better adjusted to the description of deformed D = 4 Euclidean supersymmetries with independent left-chiral and right-chiral supercharges. They lead to new quantum superspaces, obtained by the superextension of twist deformations of spacetime providing Lie-algebraic noncommutativity of space-time coordinates. In the Hopf-algebraic Euclidean SUSY framework the considered supertwist deformations provide an alternative to the