Homology and modular classes of Lie algebroids
[Classes d’homologie et classes modulaire pour les algébroïdes de Lie]
Grabowski, Janusz ; Marmo, Giuseppe ; Michor, Peter W.
Annales de l'Institut Fourier, Tome 56 (2006), p. 69-83 / Harvested from Numdam
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Pour un algébroïde de Lie, le choix des divergences à la mode classique donne une théorie de l’homologie unique. Elles définissent aussi naturellement les classes modulaires de quelques morphismes des algébroïdes de Lie. Cette méthode, appliquée à l’application d’ancre, nous permet de retrouver la classe modulaire due à S. Evens, J.-H. Lu, et A. Weinstein.

For a Lie algebroid, divergences chosen in a classical way lead to a uniquely defined homology theory. They define also, in a natural way, modular classes of certain Lie algebroid morphisms. This approach, applied for the anchor map, recovers the concept of modular class due to S. Evens, J.-H. Lu, and A. Weinstein.

Publié le : 2006-01-01
DOI : https://doi.org/10.5802/aif.2172
Classification:  17B56,  17B66,  17B70,  53C05
Mots clés: algébroïde de Lie, cohomologie de de Rham, dualité de Poincaré, divergence 
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     author = {Grabowski, Janusz and Marmo, Giuseppe and Michor, Peter W.},
     title = {Homology and modular classes of Lie algebroids},
     journal = {Annales de l'Institut Fourier},
     volume = {56},
     year = {2006},
     pages = {69-83},
     doi = {10.5802/aif.2172},
     zbl = {1141.17018},
     mrnumber = {2228680},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2006__56_1_69_0}
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Grabowski, Janusz; Marmo, Giuseppe; Michor, Peter W. Homology and modular classes of Lie algebroids. Annales de l'Institut Fourier, Tome 56 (2006) pp. 69-83. doi : 10.5802/aif.2172. http://gdmltest.u-ga.fr/item/AIF_2006__56_1_69_0/

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