54 citations · 273 across the 53 of their papers we have counts for
13 papers · 1 filter
The classical dynamic symmetry for the -Kepler problems
Sofiane Bouarroudj, Guowu Meng
For the Jordan algebra of hermitian matrices of order , we let be its submanifold consisting of rank-one semi-positive definite elements. The composition of the cotange…
Riemannian Curl in Contact Geometry
Sofiane Bouarroudj, Valentin Ovsienko
We consider a contact manifold with a pseudo-Riemannian metric and define a contact vector field intrinsically associated to this pair of structures. We call this new differential…
Minkowski superspaces and superstrings as almost real-complex supermanifolds
Sofiane Bouarroudj, Pavel Grozman, Dimitry Leites +1
In 1996/7, J. Bernstein observed that smooth or analytic supermanifolds that mathematicians study are real or (almost) complex ones, while Minkowski superspaces are completely diff…
On sl(2)-equivariant quantizations
S. Bouarroudj, M. Iyadh Ayari
By computing certain cohomology of Vect(M) of smooth vector fields we prove that on 1-dimensional manifolds M there is no quantization map intertwining the action of non-projective…
On sl(2,R)-relative cohomology of the Lie algebra of vector fields and differential operators
Sofiane Bouarroudj
Let Vect(R) be the Lie algebra of smooth vector fields on R. The space of symbols Pol(T^* R) admits a non-trivial deformation (given by differential operators on weighted densities…
Cohomology of the vector fields Lie algebras on RP^1 acting on bilinear differential operators
Sofiane Bouarroudj
The main topic of this paper is two folds. First, we compute the first relative cohomology group of the Lie algebra of smooth vector fields on the projective line, Vect(RP^1), with…
Remarks on the Schwarzian Derivatives and the Invariant Quantization by means of a Finsler Function
Sofiane Bouarroudj
Let be a Finsler manifold. We construct a 1-cocycle on $\Diff(M)$ with values in the space of differential operators acting on sections of some bundles, by means of the Fin…
Conformal Schwarzian derivatives and conformally invariant quantization
Sofiane Bouarroudj
Let be a pseudo-Riemannian manifold. We propose a new approach for defining the conformal Schwarzian derivatives. These derivatives are 1-cocycles on the group of diffeomor…
Cohomology of groups of diffeomorphims related to the modules of differential operators on a smooth manifold
Sofiane Bouarroudj
Let be a manifold and be the cotangent bundle. We introduce a 1-cocycle on the group of diffeomorphisms of with values in the space of linear differential operators…
Fromula for the Projectively Invariant Quantization on Degree Three
Sofiane Bouarroudj
We give an explicit formula for the projectively invariant quantization map between the space of symbols of degree three and the space of third-order linear differential operators,…
Projective and Conformal Schwarzian Derivatives and Cohomology of Lie Algebras Vector Fields Related to Differential Operators
Sofiane Bouarroudj
Let be either a projective manifold or a pseudo-Riemannian manifold We extend, intrinsically, the projective/conformal Schwarzian derivatives that we have int…
Projectively Equivariant Quantization Map
S. Bouarroudj
Let M be a manifold endowed with a symmetric affine connection The aim of this paper is to describe a quantization map between the space of second-order polynomials on the cot…
Schwarzian derivative related to modules of differential operators on a locally projective manifold
S. Bouarroudj, V. Ovsienko
We introduce a 1-cocycle on the group of diffeomorphisms Diff of a smooth manifold endowed with a projective connection. This cocycle represents a nontrivial cohomology cl…