Abelian simply transitive affine groups of symplectic type
[Groupes abéliens affines simplement transitifs du type symplectique]
Baues, Oliver ; Cortés, Vicente
Annales de l'Institut Fourier, Tome 52 (2002), p. 1729-1751 / Harvested from Numdam
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L'ensemble des sous-groupes abéliens simplement transitifs du groupe affine correspond, de façon naturelle, à l'ensemble des solutions réelles d'un système d'équations algébriques. Nous classifions les sous-groupes abéliens simplement transitifs du groupe symplectique affine, en construisant un modèle pour la variété de solutions correspondante. De manière similaire, nous classifions les espaces modèles globaux des variétés kählériennes spéciales, plates, avec forme cubique constante.

The set of all Abelian simply transitive subgroups of the affine group naturally corresponds to the set of real solutions of a system of algebraic equations. We classify all simply transitive subgroups of the symplectic affine group by constructing a model space for the corresponding variety of solutions. \noindent Similarly, we classify the complete global model spaces for flat special Kähler manifolds with a constant cubic form.

Publié le : 2002-01-01
DOI : https://doi.org/10.5802/aif.1932
Classification:  22E25,  22E45,  53C26
Mots clés: transformations affines, connexions symplectiques plates, variétés de Kähler spéciales 
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     author = {Baues, Oliver and Cort\'es, Vicente},
     title = {Abelian simply transitive affine groups of symplectic type},
     journal = {Annales de l'Institut Fourier},
     volume = {52},
     year = {2002},
     pages = {1729-1751},
     doi = {10.5802/aif.1932},
     mrnumber = {1952529},
     zbl = {1012.22013},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2002__52_6_1729_0}
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Baues, Oliver; Cortés, Vicente. Abelian simply transitive affine groups of symplectic type. Annales de l'Institut Fourier, Tome 52 (2002) pp. 1729-1751. doi : 10.5802/aif.1932. http://gdmltest.u-ga.fr/item/AIF_2002__52_6_1729_0/

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