The general solution of the real $Z_2^{\otimes N}$ graded contractions of $so(N+1)$

Details The general solution of the real $Z_2^{\otimes N}$ graded contractions of $so(N+1)$ The general solution of the real $Z_2^{\otimes N}$ graded contractions of $so(N+1)$

1996-01-09

arxiv.org/abs/hep-th/9601032v2

J.Phys.A29:6643-6652,1996

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, LaTeX; explicit proofs and applications to kinematical algebras are added

Scientific paper

10.1088/0305-4470/29/20/018

The general solution of the graded contraction equations for a $\zz_2^{\otimes N}$ grading of the real compact simple Lie algebra $so(N+1)$ is presented in an explicit way. It turns out to depend on $2^N-1$ independent real parameters. The structure of the general graded contractions is displayed for the low dimensional cases, and kinematical algebras are shown to appear straightforwardly. The geometrical (or physical) meaning of the contraction parameters as curvatures is also analysed; in particular, for kinematical algebras these curvatures are directly linked to geometrical properties of possible homogeneous space-times.

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