Related papers: Quantum $\kappa$-deformations of D=4 relativistic …
The $\kappa$-deformed $D=4$ Poincar{\'e} superalgebra written in Hopf superalgebra form is transformed to the basis with classical Lorentz subalgebra generators. We show that in such a basis the $\kappa$-deformed $D=4$ Poincare superalgebra…
The classical $r$-matrix for $N=1$ superPoincar{\'e} algebra, given by Lukierski, Nowicki and Sobczyk is used to describe the graded Poisson structure on the $N=1$ Poincar{\'e} supergroup. The standard correspondence principle between the…
We provide first explicite examples of quantum deformations of D=4 conformal algebra with mass-like deformation parameters, in applications to quantum gravity effects related with Planck mass. It is shown that one of the classical…
The $\kappa$-deformation of the D-dimensional Poincar\'e algebra $(D\geq 2)$ with any signature is given. Further the quadratic Poisson brackets, determined by the classical $r$-matrix are calculated, and the quantum Poincar\'e group "with…
Recent work showed that $\kappa$-deformations can describe the quantum deformation of several relativistic models that have been proposed in the context of quantum gravity phenomenology. Starting from the Poincar\'e algebra of…
We describe three ways of modifying the relativistic Heisenberg algebra - first one not linked with quantum symmetries, second and third related with the formalism of quantum groups. The third way is based on the identification of…
We show that the $\kappa$-deformed Poincar\'e quantum algebra proposed for elementary particle physics has the structure of a Hopf agebra bicrossproduct $U(so(1,3))\cobicross T$. The algebra is a semidirect product of the classical Lorentz…
We shall outline two ways of introducing the modification of Einstein's relativistic symmetries of special relativity theory - the Poincar\'{e} symmetries. The most complete way of introducing the modifications is via the noncocommutative…
We consider the simplest class of Lie-algebraic deformations of space-time algebra, with the selection of $\kappa$-deformations as providing quantum deformation of relativistic framework. We recall that the $\kappa$-deformation along any…
We review shortly present status of quantum deformations of Poincar\'{e} and conformal supersymmetries. After recalling the $\kappa$-deformation of $\hbox{D=4}$ Poincar\'{e} supersymmetries we describe the corresponding star product…
We argue that the $\kappa$-deformation is related to a factorization of a Lie group, therefore {\em an approproate version of $\kappa$-Poincar\'{e} does exist on the $C^*$-algebraic level}. The explict form of this factorization is computed…
We consider $\kappa$-deformed relativistic quantum phase space and possible implementations of the Lorentz algebra. There are two ways of performing such implementations. One is a simple extension where the Poincar\'e algebra is unaltered,…
We deform Heisenberg algebra and corresponding coalgebra by twist. We present undeformed and deformed tensor identities. Coalgebras for the generalized Poincar\'{e} algebras have been constructed. The exact universal $R$-matrix for the…
We discussed twisted quantum deformations of D=4 Lorentz and Poincare algebras. In the case of Poincare algebra it is shown that almost all classical r-matrices of S.Zakrzewski classification can be presented as a sum of subordinated…
We present the quantum $\kappa$-deformation of BMS symmetry, by generalizing the lightlike $\kappa$-Poincar\'e Hopf algebra. On the technical level, our analysis relies on the fact that the lightlike $\kappa$-deformation of Poincar\'e…
We discussed quantum deformations of D=4 Lorentz and Poincare algebras. In the case of Poincare algebra it is shown that almost all classical r-matrices of S. Zakrzewski classification correspond to twisted deformations of Abelian and…
We consider two realizations of the $\kappa$-deformed phase space obtained as a cross product algebra extension of $k$-Poincar\'{e} algebra. Two kinds of the kappa-deformed uncertainty relations are briefly discussed.
Extending the commutator algebra of quantum $\kappa$-Poincar\'e symmetry to the whole of the phase space, and assuming that this algebra is to be covariant under action of deformed Lorentz generators, we derive the transformation properties…
We present here the general solution describing generators of \kdef \poin algebra as the functions of classical \poin algebra generators as well as the inverse formulae. Further we present analogous relations for the generators of N=1 D=4…
In this Letter, 2D Dirac oscillator in the quantum deformed framework generated by the $\kappa$-Poincar\'{e}-Hopf algebra is considered. The problem is formulated using the $\kappa$-deformed Dirac equation. The resulting theory reveals that…