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

Abstract

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.

References in corpus (3)

• Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
• Three Dimensional Quantum Geometry and Deformed Poincare Symmetry
• Quantum $\kappa$-Poincaré Algebra from de Sitter Space of Momenta

Cited by in corpus (1)

• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra