The Chern character for Lie-Rinehart algebras
Algebraic Geometry
2020-11-13 v6 K-Theory and Homology
Abstract
Classical Chern-Weil theory proves existence of a ring homomorphism - the Chern character - from the Grothendieck ring of locally free finite rank A-modules to the algebraic de Rham cohomology of A. In this paper we prove existence of a ring homomorphism from the Grothendieck ring of locally free finite rank A-modules with an L-connection to the Lie-Rinehart cohomology of L, where L is a Lie-Rinehart algebra. As a corollary we get the classical Chern character.
Cite
@article{arxiv.math/0408428,
title = {The Chern character for Lie-Rinehart algebras},
author = {Helge Øystein Maakestad},
journal= {arXiv preprint arXiv:math/0408428},
year = {2020}
}
Comments
17 pages, revised version. References added. Example added in section 3