Geodesic
Reconstruction from Representations: Jacobi via Cohomology
Journal of Lie theory, Tome 27 (2017) no. 4, pp. 1141-115
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A subalgebra h of a Lie algebra g determines an h-representation ρ on m = g / h. We discuss how to reconstruct g from (h, m, ρ). In other words, we find all the ingredients for building non-reductive Klein geometries. The Lie algebra cohomology plays a decisive role here.
Classification : 17B55, 22E47, 17B05, 22F30
Mots-clés : Homogeneous space, Lie algebra cohomology, non-reductive isotropy 
@article{JLT_2017_27_4_JLT_2017_27_4_a13,
     author = {B. Kruglikov and H. Winther},
     title = {Reconstruction from {Representations:} {Jacobi} via {Cohomology}},
     journal = {Journal of Lie theory},
     pages = {1141--115},
     year = {2017},
     volume = {27},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2017_27_4_JLT_2017_27_4_a13/}
}
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B. Kruglikov; H. Winther. Reconstruction from Representations: Jacobi via Cohomology. Journal of Lie theory, Tome 27 (2017) no. 4, pp. 1141-115. http://geodesic.mathdoc.fr/item/JLT_2017_27_4_JLT_2017_27_4_a13/