Abstract
The Inönü-Wigner contractions which interrelate the Lie algebras of the isometry groups of metric spaces are discussed with reference to deformations of the absolutes of the spaces. A general formula is derived for the Lie algebra commutation relations of the isometry group for anyN-dimensional metric space. These ideas are illustrated by a discussion of important particular cases, which interrelate the four-dimensional de Sitter, Poincaré, and Galilean groups.
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Reference
Fernandez Sanjuan, M. A. (1984). Group contraction and the Nine Cayley-Klein Geometries,International Journal of Theoretical Physics,23, 1–14.
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Lord, E.A. Geometrical interpretation of Inönü-Wigner contractions. Int J Theor Phys 24, 723–730 (1985). https://doi.org/10.1007/BF00670879
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DOI: https://doi.org/10.1007/BF00670879