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

preprint2010arXivOpen access

Abstract

Different deformations of the Poincare symmetries have been identified for various non-commutative spaces (e.g. κκ-Minkowski, sl(2,R)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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