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

Understand

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.