Truncated Lie groups and almost Klein models

Georges Giraud; Michel Boyom

Open Mathematics (2004)

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

Abstract

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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.

How to cite

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Georges 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

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  8. [8] M. Nguiffo Boyom: “Déformations des structures d'algèbre de Lie tronquée”, CRAS Paris, Vol. 273, (1973), pp. 859–862. Zbl0264.17004
  9. [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. [10] A. Nijenhuis: “Deformations of Lie algebra structures”, J. Math. and Mech., Vol. 17, (1967), pp. 89–106. Zbl0166.30202
  11. [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. [12] R.S. Palais: “Global formulation of the Lie transformation groups”, Mem Amer. Math. Soc., Vol. 22, pp. 178–265. 
  13. [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. [14] J.A. Wolf: Spaces of constant curvature, 3rd ed., Mass.: Publish Perish, Inc. XV, Boston, 1974. 
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