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

[摘要] Different deformations of the Poincaré symmetries have been identified for various non-commutative spaces (e.g. κ-Minkowski, sl(2, R ), Moyal). We present here the deformation of the Poincaré 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.

[关键词] Snyder space-time;quantum group