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.

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Cited by in corpus (5)

• The principle of relative locality
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• Loop Quantum Gravity Phenomenology: Linking Loops to Observational Physics
• Tensor models and 3-ary algebras
• Non-Associative Algebras and Quantum Physics -- A Historical Perspective