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 an 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.

References


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