Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-15T23:22:02.525Z Has data issue: false hasContentIssue false
  • English
  • Français

Cohomology of the Vector Fields Lie Algebra and Modules of Differential Operators on a Smooth Manifold

Published online by Cambridge University Press:  04 December 2007

P. B. A. Lecomte  and
V. Yu. Ovsienko
P. B. A. Lecomte
Affiliation:
Institute de Mathématiques, Université de Liège, Sart Tilman, Grande Traverse, 12 (B 37), B-4000 Liège, Belgium. E-mail: [email protected]
V. Yu. Ovsienko
Affiliation:
C.N.R.S., Centre de Physique Théorique, Luminy – Case 907, F–13288 Marseille, Cedex 9, France. E-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let M be a smooth manifold, ${\cal S}$ the space of polynomial on fibers functions on T*M (i.e., of symmetric contravariant tensor fields). We compute the first cohomology space of the Lie algebra, Vect(M), of vector fields on M with coefficients in the space of linear differential operators on ${\cal S}$. This cohomology space is closely related to the Vect(M)-modules, ${\cal D}$λ(M), of linear differential operators on the space of tensor densities on M of degree λ.

Keywords

cohomologydifferential operatorsquantization
Type
Research Article
Information
Compositio Mathematica , Volume 124 , Issue 1 , October 2000 , pp. 95 - 110
Copyright
© 2000 Kluwer Academic Publishers