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.
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.
Keywords: affine transformations, flat symplectic connections, special Kähler manifolds
Mot clés : transformations affines, connexions symplectiques plates, variétés de Kähler spéciales
@article{AIF_2002__52_6_1729_0, author = {Baues, Oliver and Cort\'es, Vicente}, title = {Abelian simply transitive affine groups of symplectic type}, journal = {Annales de l'Institut Fourier}, pages = {1729--1751}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {52}, number = {6}, year = {2002}, doi = {10.5802/aif.1932}, mrnumber = {1952529}, zbl = {1012.22013}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1932/} }
TY - JOUR AU - Baues, Oliver AU - Cortés, Vicente TI - Abelian simply transitive affine groups of symplectic type JO - Annales de l'Institut Fourier PY - 2002 SP - 1729 EP - 1751 VL - 52 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1932/ DO - 10.5802/aif.1932 LA - en ID - AIF_2002__52_6_1729_0 ER -
%0 Journal Article %A Baues, Oliver %A Cortés, Vicente %T Abelian simply transitive affine groups of symplectic type %J Annales de l'Institut Fourier %D 2002 %P 1729-1751 %V 52 %N 6 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1932/ %R 10.5802/aif.1932 %G en %F AIF_2002__52_6_1729_0
Baues, Oliver; Cortés, Vicente. Abelian simply transitive affine groups of symplectic type. Annales de l'Institut Fourier, Volume 52 (2002) no. 6, pp. 1729-1751. doi : 10.5802/aif.1932. http://archive.numdam.org/articles/10.5802/aif.1932/
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