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 : 10.5802/aif.2170
Classification : 14C17, 19E15, 14L15
Keywords: Lie-Rinehart algebra, connection, de Rham cohomology, Lie-Rinehart cohomology, Jacobsons Galois correspondence, Lie-Rinehart algebra, connection, de Rham cohomology, Lie-Rinehart cohomology, Jacobsons Galois correspondence
Mot clés : algèbres de Lie-Rinehart, connexion, cohomologie de De Rham, cohomologie de Lie-Rinehart, correspondance de Galois de Jacobson.
Maakestad, Helge 1

1 Université Paris VII, Institut de Mathématiques, case 247, 4 place Jussieu, 75252 Paris Cedex (France)
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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. http://www.numdam.org/articles/10.5802/aif.2170/

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