Sur l'algèbre de Lie des sections d'un fibré en algèbres de Lie
Annales de l'Institut Fourier, Tome 30 (1980) no. 4, pp. 35-50.

On étudie la structure naturelle d’algèbre de Lie de l’espace des sections de classe C k d’un fibré localement trivial dont la fibre-type est une algèbre de Lie L; on décrit, en particulier, ses dérivations et ses automorphismes. On détermine les algèbres de Lie L pour lesquelles cette structure caractérise la structure différentiable de la base du fibré.

One studies the natural Lie algebra structure of the space of sections of class C k of a locally trivial fibre bundle whose typical fibre is a Lie algebra L; in particular, its derivations and its automorphisms are described. The algebras L for which this structure characterizes the differentiable structure of the base manifold of the bundle are determined.

@article{AIF_1980__30_4_35_0,
     author = {Lecomte, Pierre},
     title = {Sur l'alg\`ebre de Lie des sections d'un fibr\'e en alg\`ebres de Lie},
     journal = {Annales de l'Institut Fourier},
     pages = {35--50},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {30},
     number = {4},
     year = {1980},
     doi = {10.5802/aif.807},
     zbl = {0433.58002},
     mrnumber = {82h:57021},
     language = {fr},
     url = {http://archive.numdam.org/articles/10.5802/aif.807/}
}
Lecomte, Pierre. Sur l'algèbre de Lie des sections d'un fibré en algèbres de Lie. Annales de l'Institut Fourier, Tome 30 (1980) no. 4, pp. 35-50. doi : 10.5802/aif.807. http://archive.numdam.org/articles/10.5802/aif.807/

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