ar X iv : h ep - t h / 02 03 18 2 v 2 2 7 Ju n 20 03 κ - deformations of D = 4 Weyl and conformal symmetries ∗

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 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. PACS numbers:11.30.Cp, 95.85.Gn, 98.70.Vc. ∗Supported by KBN grant No 5PO3B05620 (JL and MM) and by the Russian Foundation for Basic Research under grant No 00-01-00500 (VL).