70 citations · 395 across the 55 of their papers we have counts for
8 papers · 1 filter
Shadows of rationals and irrationals: supersymmetric continued fractions and the super modular group
Charles H. Conley, Valentin Ovsienko
This paper is an attempt to apply the tools of supergeometry to arithmetic. Supergeometric objects are defined over supercommutative rings of coefficients, and we consider an integ…
Linear differential operators on contact manifolds
Charles H. Conley, Valentin Ovsienko
We consider differential operators between sections of arbitrary powers of the determinant line bundle over a contact manifold. We extend the standard notions of the Heisenberg cal…
Graded commutative algebras: examples, classification, open problems
Sophie Morier-Genoud, Valentin Ovsienko
We consider $\G$-graded commutative algebras, where $\G$ is an abelian group. Starting from a remarkable example of the classical algebra of quaternions and, more generally, an arb…
Lie antialgebras: cohomology and representations
Valentin Ovsienko
We describe the main algebraic and geometric properties of the class of algebras introduced in [arXiv:0705.1629]. We discuss their origins in symplectic geometry and associative al…
Bi-Hamiltonian nature of the equation
Valentin Ovsienko
We study non-linear integrable partial differential equations naturally arising as bi-Hamiltonian Euler equations related to the looped cotangent Virasoro algebra. This infinite-di…
Supertransvectants and symplectic geometry
Hichem Gargoubi, Valentin Ovsienko
We consider the -invariant bilinear operations on weighted densities on the supercircle called the supertransvectants. These operations are analogues of the fam…
Differential operators on supercircle: conformally equivariant quantization and symbol calculus
Hichem Gargoubi, Najla Mellouli, Valentin Ovsienko
We consider the supercircle equipped with the standard contact structure. The conformal Lie superalgebra K(1) acts on as the Lie superalgebra of contact vector…
Large Coadjoint representation of Virasoro-type Lie algebras and differential operators on tensor-densities
Valentin Ovsienko
We discuss the geometrical nature of the coadjoint representation of the Virasoro algebra and some of its generalizations. The isomorphism of the coadjoint representation of the Vi…