nLab locally Klein geometry




Representation theory



Generalising a Klein geometry, a locally Klein geometry is a triple (Γ,G,H)(\Gamma, G,H) where G/HG/H is a Klein geometry (not necessarily connected) and ΓG\Gamma \subset G is a discrete subgroup acting by left multiplication on the coset space G/HG/H as a group of covering transformations with the double coset space, Γ\G/H\Gamma \backslash G/H, connected (Sharpe 97, Def. 3.10, Sharpe 02, Def. 2.7).


  • Richard Sharpe, Differential geometry: Cartan’s generalization of Klein’s Erlangen program, Graduate Texts in Mathematics, vol. 166, Springer-Verlag, 1997.

  • Richard Sharpe, An introduction to Cartan Geometries, in: Jan Slovák, Martin Čadek (eds.): Proceedings of the 21st Winter School “Geometry and Physics”. Circolo Matematico di Palermo, Palermo, 2002. Rendiconti del Circolo Matematico di Palermo, Serie II, Supplemento No. 69. pp. [61]–75 (EuDML)

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