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

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.

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.

@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},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {30},
     number = {4},
     year = {1980},
     pages = {35-50},
     doi = {10.5802/aif.807},
     zbl = {0433.58002},
     mrnumber = {82h:57021},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1980__30_4_35_0}
}
Lecomte, Pierre. Sur l'algèbre de Lie des sections d'un fibré en algèbres de Lie. Annales de l'Institut Fourier, Volume 30 (1980) no. 4, pp. 35-50. doi : 10.5802/aif.807. http://www.numdam.org/item/AIF_1980__30_4_35_0/

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