no. 6
Abelian simply transitive affine groups of symplectic type
[Groupes abéliens affines simplement transitifs du type symplectique]
Baues, Oliver1 ; Cortés, Vicente2
1 ETH-Zürich, Departement Mathematik, Rämistrasse 101, Ch-8092 Zürich
2 Université de Nancy I, Institut Élie Cartan, BP 239 54506 Vandoeuvre-les-Nancy Cedex (France)
Annales de l'Institut Fourier, Tome 52 (2002) no. 6, pp. 1729-1751.

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.

DOI : 10.5802/aif.1932
Classification : 22E25, 22E45, 53C26
Keywords: affine transformations, flat symplectic connections, special Kähler manifolds
Mot clés : transformations affines, connexions symplectiques plates, variétés de Kähler spéciales

Baues, Oliver 1 ; Cortés, Vicente 2

1 ETH-Zürich, Departement Mathematik, Rämistrasse 101, Ch-8092 Zürich
2 Université de Nancy I, Institut Élie Cartan, BP 239 54506 Vandoeuvre-les-Nancy Cedex (France) 
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Baues, Oliver; Cortés, Vicente. Abelian simply transitive affine groups of symplectic type. Annales de l'Institut Fourier, Tome 52 (2002) no. 6, pp. 1729-1751. doi : 10.5802/aif.1932. https://aif.centre-mersenne.org/articles/10.5802/aif.1932/

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