4 papers · 2 filters
Methods of Equivariant Quantization
C. Duval, P. Lecomte, V. Ovsienko
This article is a survey of recent work of the authors developing a new approach to quantization based on the equivariance with respect to some Lie group of symmetries. Examples ar…
Cohomology of the vector fields Lie algebra and modules of differential operators on a smooth manifold
P. B. A. Lecomte, V. Yu. Ovsienko
Let be a smooth manifold, the space of polynomial on fibers functions on (i.e., of symmetric contravariant tensor fields). We compute the first cohomology space…
Conformally equivariant quantization: Existence and uniqueness
C. Duval, P. Lecomte, V. Ovsienko
We prove the existence and the uniqueness of a conformally equivariant symbol calculus and quantization on any conformally flat pseudo-Riemannian manifold $(M,\rg)$. In other words…
A remark about the Lie algebra of infinitesimal conformal transformations of the Euclidian space
F. Boniver, P. B. A. Lecomte
Infinitesimal conformal transformations of are always polynomial and finitely generated when . Here we prove that the Lie algebra of infinitesimal conformal polynomial t…