On a Lie Algebraic Characterization of Vector Bundles

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2012
• Main Authors: B.A. Lecomte, P., Leuther, T., Mushengezi, E.Z.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2012
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148364
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On a Lie Algebraic Characterization of Vector Bundles / P. B.A. Lecomte, T. Leuther, E.Z. Mushengezi // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 8 назв. — англ.

We prove that a vector bundle π: E→M is characterized by the Lie algebra generated by all differential operators on E 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 f...