We know some nice spacetime have a lot of symmetries. It is said that

  • Minkowski spacetime has $$ISO(d-1,1)/SO(d-1,1),$$

  • de Sitter spacetime has $$SO(d,1)/SO(d-1,1)$$ and

  • anti-de Sitter spacetime has $$SO(d-1,2)/SO(d-1,1).$$

e.g. see https://physics.stackexchange.com/a/75604/42982

Question: Is this correct that the above is the precise full symmetry of Minkowski, de Sitter spacetime, and anti-de Sitter spacetime? It this the same as the isometry of these spacetimes? How to show this is the complete symmetry?

  • $\begingroup$ The proof of this can be found in Wolf's "Spaces of Constant Curvature", for instance. $\endgroup$ – Slereah Sep 24 '19 at 6:40

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