11 papers
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…
Real numbers having ultimately periodic representations in abstract numeration systems
P. Lecomte, M. Rigo
Using a genealogically ordered infinite regular language, we know how to represent an interval of R. Numbers having an ultimately periodic representation play a special role in cla…
On the Cohomology of the spaces of differential operators acting on skewsymmetric tensor fields or on forms, as modules of the Lie algebra of vector fields
B. Agrebaoui, F. Ammar, P. Lecomte
The space of differential operators acting on skewsymmetric tensor fields or on smooth forms of a smooth manifold are representations of its Lie algebra of vector fields. We comput…
Multi-parameter deformations of the module of symbols of differential operators
F. Ammar, B. Agrebaoui, V. Ovsienko
The space of symbols of differential operators on a smooth manifold (i.e., the space of symmetric contravariant tensor fields) is naturally a module over the Lie algebra of vector…
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…