In physics and mathematics, the κ-Poincaré algebra, named after Henri Poincaré, is a deformation of the Poincaré algebra into a Hopf algebra. In the bicrossproduct basis, introduced by Majid-Ruegg[1] its commutation rules reads:

Where are the translation generators, the rotations and the boosts. The coproducts are:

The antipodes and the counits:

The κ-Poincaré algebra is the dual Hopf algebra to the κ-Poincaré group, and can be interpreted as its “infinitesimal” version.

References

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  1. ^ Majid, S.; Ruegg, H. (1994). "Bicrossproduct structure of κ-Poincare group and non-commutative geometry". Physics Letters B. 334 (3–4). Elsevier BV: 348–354. arXiv:hep-th/9405107. Bibcode:1994PhLB..334..348M. doi:10.1016/0370-2693(94)90699-8. ISSN 0370-2693.