[Le caractère de Chern pour les algèbres de Lie-Rinehart]
Soit une -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 sur à valeurs dans la cohomologie de Lie-Rinehart de , qui est indépendante d’un choix de -connexion. Notre résultat établit une généralisation du caractère de Chern classique en -théorie à la cohomologie de De Rham algébrique.
Let be a commutative -algebra where is a ring containing the rationals. We prove the existence of a Chern character for Lie-Rinehart algebras over A with values in the Lie-Rinehart cohomology of L which is independent of choice of a -connection. Our result generalizes the classical Chern character from the -theory of to the algebraic De Rham cohomology.
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.
@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{\textquoteright}institut Fourier},
volume = {55},
number = {7},
year = {2005},
doi = {10.5802/aif.2170},
mrnumber = {2207393},
zbl = {1097.14004},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2170/}
}
TY - JOUR AU - Maakestad, Helge TI - The Chern character for Lie-Rinehart algebras JO - Annales de l'Institut Fourier PY - 2005 SP - 2551 EP - 2574 VL - 55 IS - 7 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2170/ DO - 10.5802/aif.2170 LA - en ID - AIF_2005__55_7_2551_0 ER -
%0 Journal Article %A Maakestad, Helge %T The Chern character for Lie-Rinehart algebras %J Annales de l'Institut Fourier %D 2005 %P 2551-2574 %V 55 %N 7 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2170/ %R 10.5802/aif.2170 %G en %F 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. http://www.numdam.org/articles/10.5802/aif.2170/
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