Derivations of the Lie algebras of differential operators

Citations of this article
Mendeley users who have this article in their library.


This paper encloses a complete and explicit description of the derivations of the Lie algebra D(M)of all linear differential operators of a smooth manifold M, of its Lie subalgebra D1(M) of all linear first-order differential operators of M, and of the Poisson algebra S(M) = Pol(T*M) of all polynomial functions on T*M, the symbols of the operators in D(M). It turns out that, in terms of the Chevalley cohomology, H1(D(M), D(M)) = HDR1(M), H1 (D1(M), D1(M)) = HDR1(M) ⊕ R2, and H1(S(M), S(M)) = HDR1 (M) ⊕ R. The problem of distinguishing those derivations that generate one-parameter groups of automorphisms and describing these one-parameter groups is also solved.




Grabowski, J., & Poncin, N. (2005). Derivations of the Lie algebras of differential operators. Indagationes Mathematicae, 16(2), 181–200.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free