Poisson cohomology and quantization.
Poisson geometry and deformation quantization near a strictly pseudoconvex boundary
Let be a complex manifold with strongly pseudoconvex boundary . If is a defining function for , then is plurisubharmonic on a neighborhood of in , and the (real) 2-form is a symplectic structure on the complement of in a neighborhood of in ; it blows up along . The Poisson structure obtained by inverting extends smoothly across and determines a contact structure on which is the same as the one induced by the complex structure. When is compact, the Poisson structure near...
Poisson geometry of directed networks in an annulus
As a generalization of Postnikov’s construction [P], we define a map from the space of edge weights of a directed network in an annulus into a space of loops in the Grassmannian. We then show that universal Poisson brackets introduced for the space of edge weights in [GSV3] induce a family of Poisson structures on rational matrix-valued functions and on the space of loops in the Grassmannian. In the former case, this family includes, for a particular kind of networks, the Poisson bracket associated...
Poisson manifolds, Lie algebroids, modular classes: a survey.
Poisson structures on having only two symplectic leaves: the origin and the rest
Examples of Poisson structures with isolated non-symplectic points are constructed from classical r-matrices.
Poisson structures on cotangent bundles.
Poisson structures on Weil bundles.
Poisson-Lie groupoids and the contraction procedure
On the level of Lie algebras, the contraction procedure is a method to create a new Lie algebra from a given Lie algebra by rescaling generators and letting the scaling parameter tend to zero. One of the most well-known examples is the contraction from 𝔰𝔲(2) to 𝔢(2), the Lie algebra of upper-triangular matrices with zero trace and purely imaginary diagonal. In this paper, we will consider an extension of this contraction by taking also into consideration the natural bialgebra structures on these...
Poisson–Lie sigma models on Drinfel’d double
Poisson sigma models represent an interesting use of Poisson manifolds for the construction of a classical field theory. Their definition in the language of fibre bundles is shown and the corresponding field equations are derived using a coordinate independent variational principle. The elegant form of equations of motion for so called Poisson-Lie groups is derived. Construction of the Poisson-Lie group corresponding to a given Lie bialgebra is widely known only for coboundary Lie bialgebras. Using...
Polynomial structures with double roots
Poznámka k vypočítání obsahu trojbokého hranolu šikmého
Poznámka o sférické trigonometrii
Projective structure, and the symplectic Dirac operator
Inspired by the results on symmetries of the symplectic Dirac operator, we realize symplectic spinor fields and the symplectic Dirac operator in the framework of (the double cover of) homogeneous projective structure in two real dimensions. The symmetry group of the homogeneous model of the double cover of projective geometry in two real dimensions is .
Projectively equivariant quantization and symbol on supercircle
Let be the space of linear differential operators on weighted densities from to as module over the orthosymplectic Lie superalgebra , where , is the space of tensor densities of degree on the supercircle . We prove the existence and uniqueness of projectively equivariant quantization map from the space of symbols to the space of differential operators. An explicite expression of this map is also given.
Prolongation of Poisson -form on Weil bundles
In this paper, denotes a smooth manifold of dimension , a Weil algebra and the associated Weil bundle. When is a Poisson manifold with -form , we construct the -Poisson form , prolongation on of the -Poisson form . We give a necessary and sufficient condition for that be an -Poisson manifold.
Proof of the Knop conjecture
In this paper we prove the Knop conjecture asserting that two smooth affine spherical varieties with the same weight monoid are equivariantly isomorphic. We also state and prove a uniqueness property for (not necessarily smooth) affine spherical varieties.
Proper groupoids and momentum maps : linearization, affinity, and convexity
Properties of Pseudo-holomorphic Curves in Symplectisations II: Embedding Controls and Algebraic Invariants.
Properties of pseudoholomorphic curves in symplectisations. I : asymptotics
Propriétés ergodiques, en mesure infinie, de certains systèmes dynamiques fibrés