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arXiv · hep-th/9405107

Bicrossproduct structure of $κ$-Poincare group and non-commutative geometry

Shahn Majid·Henri Ruegg
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Abstract

We show that the $κ$-deformed Poincaré quantum algebra proposed for elementary particle physics has the structure of a Hopf agebra bicrossproduct $U(so(1,3))\cobicross T$. The algebra is a semidirect product of the classical Lorentz group $so(1,3)$ acting in a deformed way on the momentum sector $T$. The novel feature is that the coalgebra is also semidirect, with a backreaction of the momentum sector on the Lorentz rotations. Using this, we show that the $κ$-Poincaré acts covariantly on a $κ$-Minkowski space, which we introduce. It turns out necessarily to be deformed and non-commutative. We also connect this algebra with a previous approach to Planck scale physics.

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Shahn Majid, Henri Ruegg. 1994-05-20. Bicrossproduct structure of $κ$-Poincare group and non-commutative geometry. https://doi.org/10.1016/0370-2693(94)90699-8

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