\kappa-deformations of D=4 Weyl and conformal symmetries

Abstract

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 $r$-matrices defined on the Borel subalgebra of $sl(4)$ with $o(4,2)$ reality conditions describes the light-cone $\kappa$-deformation of D=4 Poincar\'{e} algebra. We embed this deformation into the three-parameter family of generalized $\kappa$-deformations, with $r$-matrices depending additionally on the dilatation generator. Using the extended Jordanian twists framework we describe these deformations in the form of noncocommutative Hopf algebra. We describe also another four-parameter class of generalized $\kappa$-deformations, which is obtained by continuous deformation of distinguished $\kappa$-deformation of D=4 Weyl algebra, called here the standard $\kappa$-deformation of Weyl algebra.