The Chern character for Lie-Rinehart algebras  [ Le caractère de Chern pour les algèbres de Lie-Rinehart ]
Annales de l'Institut Fourier, Tome 55 (2005) no. 7, pp. 2551-2574.

Soit A une S-algèbre commutative, où S désigne un anneau contenant les nombres rationnels. Nous démontrons l’existence d’un caractère de Chern pour les algèbres de Lie L sur A à valeurs dans la cohomologie de Lie-Rinehart de L, qui est indépendante d’un choix de L-connexion. Notre résultat établit une généralisation du caractère de Chern classique en K-théorie à la cohomologie de De Rham algébrique.

Let A be a commutative S-algebra where S is a ring containing the rationals. We prove the existence of a Chern character for Lie-Rinehart algebras L over A with values in the Lie-Rinehart cohomology of L which is independent of choice of a L-connection. Our result generalizes the classical Chern character from the K-theory of A to the algebraic De Rham cohomology.

DOI : https://doi.org/10.5802/aif.2170
Classification : 14C17,  19E15,  14L15
Mots clés: algèbres de Lie-Rinehart, connexion, cohomologie de De Rham, cohomologie de Lie-Rinehart, correspondance de Galois de Jacobson.
@article{AIF_2005__55_7_2551_0,
     author = {Maakestad, Helge},
     title = {The Chern character for Lie-Rinehart algebras},
     journal = {Annales de l'Institut Fourier},
     pages = {2551--2574},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {55},
     number = {7},
     year = {2005},
     doi = {10.5802/aif.2170},
     zbl = {1097.14004},
     mrnumber = {2207393},
     language = {en},
     url = {aif.centre-mersenne.org/item/AIF_2005__55_7_2551_0/}
}
Maakestad, Helge. The Chern character for Lie-Rinehart algebras. Annales de l'Institut Fourier, Tome 55 (2005) no. 7, pp. 2551-2574. doi : 10.5802/aif.2170. https://aif.centre-mersenne.org/item/AIF_2005__55_7_2551_0/

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