Quantum deformations of conformal algebras introducing fundamental mass parameters

We consider a new class of classical r-matrices for D = 3 and D = 4 conformal Lie algebras. There r-matrices do satisfy the classical Yang-Baxter equation and as two-tensors belong to the tensor product of Borel subalgebra. In such a way we generalize the lowest order of known nonstandard quantum deformation of sl(2) to the Lie algebras sp(4) ≅ so(5) and sl(4) ≅ so(6). As an exercise we interpret nonstandard deformation of sl(2) as describing quantum D = 1 conformal algebra with fundamental mass parameter. Further we describe the D = 3 and D = 4 conformal bialgebras with deformation parameters equal to the inverse of fundamental masses. It appears that for D = 4 the deformation of the Poincaré algebra sector coincides with “null plane” quantum Poincaré algebra.