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Bicrossproduct structure of kappa-Poincare group and non-commutative geometry

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arxiv hep-th/9405107 v2 pith:S44T5Z4V submitted 1994-05-17 hep-th math.QA

Bicrossproduct structure of kappa-Poincare group and non-commutative geometry

classification hep-th math.QA
keywords kappaalgebradeformedbicrossproductgrouplorentzmomentumnon-commutative
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We show that the $\kappa$-deformed Poincar\'e 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 $\kappa$-Poincar\'e acts covariantly on a $\kappa$-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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Cited by 9 Pith papers

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