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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.