# Truncated Lie groups and almost Klein models

Open Mathematics (2004)

- Volume: 2, Issue: 5, page 884-898
- ISSN: 2391-5455

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topGeorges Giraud, and Michel Boyom. "Truncated Lie groups and almost Klein models." Open Mathematics 2.5 (2004): 884-898. <http://eudml.org/doc/268704>.

@article{GeorgesGiraud2004,

abstract = {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.},

author = {Georges Giraud, Michel Boyom},

journal = {Open Mathematics},

keywords = {Primary: 54H15, 57S20; Secondary: 22E15, 22E20, 58H10},

language = {eng},

number = {5},

pages = {884-898},

title = {Truncated Lie groups and almost Klein models},

url = {http://eudml.org/doc/268704},

volume = {2},

year = {2004},

}

TY - JOUR

AU - Georges Giraud

AU - Michel Boyom

TI - Truncated Lie groups and almost Klein models

JO - Open Mathematics

PY - 2004

VL - 2

IS - 5

SP - 884

EP - 898

AB - 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.

LA - eng

KW - Primary: 54H15, 57S20; Secondary: 22E15, 22E20, 58H10

UR - http://eudml.org/doc/268704

ER -

## References

top- [1] D. Bernard: “Sur la géométrie différentielle des G-structures”, Ann. Institut Fourier, Vol. 10, (1960), pp. 151–270. Zbl0095.36406
- [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 Zbl0031.24803
- [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 Zbl0121.38801
- [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 Zbl0182.36402
- [6] S. Kobayashi, K. Nagano: “Filtred Lie algebras and geometric structures III”, J. of Math. and Mech., Vol. 14, (1965), pp. 679–706. Zbl0163.28103
- [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 Zbl0097.38803
- [8] M. Nguiffo Boyom: “Déformations des structures d'algèbre de Lie tronquée”, CRAS Paris, Vol. 273, (1973), pp. 859–862. Zbl0264.17004
- [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. Zbl0166.30202
- [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. Zbl0277.58008
- [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 Zbl0157.52102

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