On a Lie Algebraic Characterization of Vector Bundles
Differential Geometry
2012-01-27 v2
Abstract
We prove that a vector bundle is characterized by the Lie algebra generated by all differential operators on which are eigenvectors of the Lie derivative in the direction of the Euler vector field. Our result is of Pursell-Shanks type but it is remarkable in the sense that it is the whole fibration that is characterized here. The proof relies on a theorem of [Lecomte P., J. Math. Pures Appl. (9) 60 (1981), 229-239] and inherits the same hypotheses. In particular, our characterization holds only for vector bundles of rank greater than 1.
Cite
@article{arxiv.1109.4772,
title = {On a Lie Algebraic Characterization of Vector Bundles},
author = {Pierre B. A. Lecomte and Thomas Leuther and Elie Zihindula Mushengezi},
journal= {arXiv preprint arXiv:1109.4772},
year = {2012}
}