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

  • M. Mozrzymas
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.

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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

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تاریخ انتشار 2003