κ-Deformations of D=4 Weyl and conformal symmetries

We provide first explicit 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 κ-deformation of D=4 Poincaré algebra. We embed this deformation into the three-parameter family of generalized κ-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 κ-deformations, which is obtained by continuous deformation of distinguished κ-deformation of D=4 Weyl algebra, called here the standard κ-deformation of Weyl algebra.