Snyder Space-Time: K-Loop and Lie Triple System

Details Snyder Space-Time: K-Loop and Lie Triple System Snyder Space-Time: K-Loop and Lie Triple System

2010-09-24

arxiv.org/abs/1009.4762v1

SIGMA 6:074,2010

Physics

Mathematical Physics

Scientific paper

10.3842/SIGMA.2010.074

Different deformations of the Poincare symmetries have been identified for various non-commutative spaces (e.g. $\kappa$-Minkowski, $sl(2,R)$, Moyal). We present here the deformation of the Poincare symmetries related to Snyder space-time. The notions of smooth "K-loop", a non-associative generalization of Abelian Lie groups, and its infinitesimal counterpart given by the Lie triple system are the key objects in the construction.

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