κ-deformations of D=3 conformal versus deformations of D=4 AdS symmetries

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We describe the classical o(3,2) r-matrices as generating the quantum deformations of either D=3 conformal algebra with mass-like deformation parameters or D=4 AdS algebra with dimensionless deformation parameters. We describe the quantization of classical o(3,2) r-matrices via Drinfeld twist method which locates the deformation in the coalgebra sector. Further we obtain the quantum o(3,2) algebra in a convenient Hopf algebra form by considering suitable deformation maps from classical to deformed o(3,2) algebra basis. It appears that if we pass from κ-deformed D =3 conformal algebra basis to the deformed D=4 AdS generators basis the role of dimensionfull parameter is taken over by the AdS radius R. We provide also the bilinear o(3,2) Casimir which we express using the deformed D=3 conformal basis.