K-Poincaré group

In physics and mathematics, the κ-Poincaré group, named after Henri Poincaré, is a quantum group, obtained by deformation of the Poincaré group into a Hopf algebra. It is generated by the elements and with the usual constraint: where is the Minkowskian metric: The commutation rules reads: In the (1 + 1)-dimensional case the commutation rules between and are particularly simple. The Lorentz generator in this case is: and the commutation rules reads: The coproducts are classical, and encode the group composition law: Also the antipodes and the counits are classical, and represent the group inversion law and the map to the identity: The κ-Poincaré group is the dual Hopf algebra to the K-Poincaré algebra, and can be interpreted as its “finite” version.