Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 074, 19 pages      arXiv:1009.4762      https://doi.org/10.3842/SIGMA.2010.074
Contribution to the Special Issue “Noncommutative Spaces and Fields”

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

Florian Girelli
School of Physics, The University of Sydney, Sydney, New South Wales 2006, Australia

Received April 29, 2010, in final form September 13, 2010; Published online September 24, 2010

Abstract
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.

Key words: Snyder space-time; quantum group.

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