22 citations · 69 across the 18 of their papers we have counts for
18 papers
Classical Poisson algebra of a vector bundle : Lie-algebraic characterization
P. B. A Lecomte, Elie Zihindula Mushengezi
We prove that the Lie algebra of symbols of linear operators acting on smooth sections of a vector bundle characterizes it. To obtain this…
Lie algebra of homogeneous operators of a vector bundle
P. B. A. Lecomte, Elie Zihindula Mushengezi
We prove that for a vector bundle , the Lie algebra generated by all differential operators on which are eigenvectors of $L_{\mathcal{E…
On Pursell-Shanks type results
Pierre B. A. Lecomte, Elie Zihindula Mushengezi
We prove a Lie-algebraic characterization of vector bundle for the Lie algebra seen as module, of all linear operators acting on sections of…
On a Lie Algebraic Characterization of Vector Bundles
Pierre B. A. Lecomte, Thomas Leuther, Elie Zihindula Mushengezi
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 di…
Alternated Hochschild Cohomology
Pierre B. A. Lecomte, Valentin Ovsienko
In this paper we construct a graded Lie algebra on the space of cochains on a $\mathbbZ_2$-graded vector space that are skew-symmetric in the odd variables. The Lie bracket is obta…
Affine representations of Lie algebras and geometric interpretation in the case of smooth manifolds
Sarah Hansoul, Pierre B. A. Lecomte
In order to understand the structure of the cohomologies involved in the study of projectively equivariant quantizations, we introduce a notion of affine representation of a Lie al…