Let be a free graded connected differential Lie algebra over the field of rational numbers. An ideal in the Lie algebra is called nice if, for every cycle such that belongs to , the kernel of the map , , is contained in . We show that the center of is a nice ideal and we give in that case some informations on the structure of the Lie algebra . We apply this computation for the determination of the rational homotopy Lie algebra of a simply connected space . We deduce that the kernel of the map induced by the attachment of a cell along an element in the center is contained in the center.
Soit une algèbre de Lie différentielle graduée définie sur le corps des nombres rationnels. Un idéal dans l’algèbre de Lie est dit gentil si pour tout cycle dont la classe appartient à contient le noyau de l’application . Nous montrons que le centre de est un gentil idéal et nous donnons dans ce cas des informations sur la structure de . Ceci est ensuite appliqué à l’étude de la structure de l’algèbre de Lie d’homotopie rationnelle d’un CW complexe simplement connexe .
@article{AIF_1996__46_1_263_0, author = {F\'elix, Yves}, title = {The center of a graded connected {Lie} algebra is a nice ideal}, journal = {Annales de l'Institut Fourier}, pages = {263--278}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {46}, number = {1}, year = {1996}, doi = {10.5802/aif.1513}, mrnumber = {97d:55021}, zbl = {0836.55005}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1513/} }
TY - JOUR AU - Félix, Yves TI - The center of a graded connected Lie algebra is a nice ideal JO - Annales de l'Institut Fourier PY - 1996 SP - 263 EP - 278 VL - 46 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1513/ DO - 10.5802/aif.1513 LA - en ID - AIF_1996__46_1_263_0 ER -
%0 Journal Article %A Félix, Yves %T The center of a graded connected Lie algebra is a nice ideal %J Annales de l'Institut Fourier %D 1996 %P 263-278 %V 46 %N 1 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1513/ %R 10.5802/aif.1513 %G en %F AIF_1996__46_1_263_0
Félix, Yves. The center of a graded connected Lie algebra is a nice ideal. Annales de l'Institut Fourier, Volume 46 (1996) no. 1, pp. 263-278. doi : 10.5802/aif.1513. http://archive.numdam.org/articles/10.5802/aif.1513/
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