We consider a real analytic dynamical system G×M→M with nonempty fixed point subset M G. Using symmetries of G×M→M, we give some conditions which imply the existence of transitive Lie transformation group with G as isotropy subgroup.
@article{bwmeta1.element.doi-10_2478_BF02475983,
author = {Georges Giraud and Michel Boyom},
title = {Truncated Lie groups and almost Klein models},
journal = {Open Mathematics},
volume = {2},
year = {2004},
pages = {884-898},
zbl = {1128.54021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475983}
}
Georges Giraud; Michel Boyom. Truncated Lie groups and almost Klein models. Open Mathematics, Tome 2 (2004) pp. 884-898. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475983/
[1] D. Bernard: “Sur la géométrie différentielle des G-structures”, Ann. Institut Fourier, Vol. 10, (1960), pp. 151–270. | Zbl 0095.36406
[2] C. Chevalley and Eilenberg: “The cohomology theory of Lie groups and Lie algebras”, Trans. Amer. Math. Soc., VOl. 63, (1948), pp. 85–124. http://dx.doi.org/10.2307/1990637 | Zbl 0031.24803
[3] C. Fredfield: “A conjecture concerning transitive subalgebra of Lie algebras”, Bull of the Amer. Math. Soc., Vol. 76, (1970), pp. 331–333.
[4] V.W. Guillemin, S. Sternberg: “An algebraic model for transitive differential geometry”, Bull of the Amer. Math. Soc., Vol. 70, (1964), pp. 16–47. http://dx.doi.org/10.1090/S0002-9904-1964-11019-3 | Zbl 0121.38801
[5] I. Hayashi: “Embedding and existence theorem of infinite Lie algebras”, J. of Math. Soc. of Japan, Vol. 22, (1970), pp. 1–14. http://dx.doi.org/10.2969/jmsj/02210001 | Zbl 0182.36402
[6] S. Kobayashi, K. Nagano: “Filtred Lie algebras and geometric structures III”, J. of Math. and Mech., Vol. 14, (1965), pp. 679–706. | Zbl 0163.28103
[7] J.L. Koszul: “Multiplicateurs et classes caractéristiques”, Trans. Amer. Math. Soc., Vol. 89, (1958), pp. 256–266. http://dx.doi.org/10.2307/1993142 | Zbl 0097.38803
[8] M. Nguiffo Boyom: “Déformations des structures d'algèbre de Lie tronquée”, CRAS Paris, Vol. 273, (1973), pp. 859–862. | Zbl 0264.17004
[9] M. Nguiffo Boyom: “Weakley maximal submodules of some S(V)-modules, Geometric applications”, Indaga Math., Vol. 1, (1990), pp. 179–200. http://dx.doi.org/10.1016/0019-3577(90)90004-7
[10] A. Nijenhuis: “Deformations of Lie algebra structures”, J. Math. and Mech., Vol. 17, (1967), pp. 89–106. | Zbl 0166.30202
[11] A.L. Onishchik (ed.) Lie groups and Lie algebras I. Foundations of Lie theory. Lie transformation groups. in Encyclopaedia of Mathematical Sciences. Vol. 20, Springer-Verlag. Berlin, 1993.
[12] R.S. Palais: “Global formulation of the Lie transformation groups”, Mem Amer. Math. Soc., Vol. 22, pp. 178–265.
[13] I.M. Singer and S. Sternberg: “The infinite groups of Lie and Cartan”, Jour. Analyse Math. Jerusalem, Vol. 15, (1965), pp. 1–114. | Zbl 0277.58008
[14] J.A. Wolf: Spaces of constant curvature, 3rd ed., Mass.: Publish Perish, Inc. XV, Boston, 1974.
[15] J.A. Wolf: “The geometry and structure of isotropic irreducible homogeneous spaces”, Acta Math., Vol. 120, (1968), pp. 59–148. http://dx.doi.org/10.1007/BF02394607 | Zbl 0157.52102