Girelli, Florian Snyder space-time: K-loop and Lie triple system. (English) Zbl 1220.81145 SIGMA, Symmetry Integrability Geom. Methods Appl. 6, Paper 074, 19 p. (2010). Summary: Different deformations of the Poincaré symmetries have been identified for various non-commutative spaces (e.g. \(\kappa \)-Minkowski, \(\mathfrak{sl}(2, \mathbb R)\), 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. Cited in 2 Documents MSC: 81R60 Noncommutative geometry in quantum theory 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory 81T75 Noncommutative geometry methods in quantum field theory Keywords:Snyder space-time; quantum group PDFBibTeX XMLCite \textit{F. Girelli}, SIGMA, Symmetry Integrability Geom. Methods Appl. 6, Paper 074, 19 p. (2010; Zbl 1220.81145) Full Text: DOI arXiv EuDML