ar X iv : h ep - t h / 03 01 05 6 v 2 2 3 Ja n 20 03 κ - Deformations of D = 3 Conformal Versus Deformations of D = 4 AdS Symmetries
نویسنده
چکیده
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.
منابع مشابه
ar X iv : h ep - t h / 03 01 05 6 v 1 9 J an 2 00 3 κ - Deformations of D = 3 Conformal Versus Deformations of D = 4 AdS Symmetries
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) a...
متن کاملar 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 ...
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