416 research outputs found
Poisson actions up to homotopy and their quantization
Symmetries of Poisson manifolds are in general quantized just to symmetries
up to homotopy of the quantized algebra of functions. It is therefore
interesting to study symmetries up to homotopy of Poisson manifolds. We notice
that they are equivalent to Poisson principal bundles and describe their
quantization to symmetries up to homotopy of the quantized algebras of
functions.Comment: 8 page
On the C-numerical range of a matrix
AbstractGiven two n × n complex matrices C and T, we prove that if the differentiable mapping q: U(n,C) → R2 defined by q(U) = tr(CU∗TU) is of rank at most 1 on a nonempty open set, then the C-numerical range W(C,T) of T is a line segment. The same conclusion holds whenever the interior of W(C,T) is empty
Superintegrable Hamiltonian systems with noncompact invariant submanifolds. Kepler system
The Mishchenko-Fomenko theorem on superintegrable Hamiltonian systems is
generalized to superintegrable Hamiltonian systems with noncompact invariant
submanifolds. It is formulated in the case of globally superintegrable
Hamiltonian systems which admit global generalized action-angle coordinates.
The well known Kepler system falls into two different globally superintegrable
systems with compact and noncompact invariant submanifolds.Comment: 23 page
Jacobi Structures in
The most general Jacobi brackets in are constructed after
solving the equations imposed by the Jacobi identity. Two classes of Jacobi
brackets were identified, according to the rank of the Jacobi structures. The
associated Hamiltonian vector fields are also constructed
Generalized n-Poisson brackets on a symplectic manifold
On a symplectic manifold a family of generalized Poisson brackets associated
with powers of the symplectic form is studied. The extreme cases are related to
the Hamiltonian and Liouville dynamics. It is shown that the Dirac brackets can
be obtained in a similar way.Comment: Latex, 10 pages, to appear in Mod. Phys. Lett.
Poisson sigma models and symplectic groupoids
We consider the Poisson sigma model associated to a Poisson manifold. The
perturbative quantization of this model yields the Kontsevich star product
formula. We study here the classical model in the Hamiltonian formalism. The
phase space is the space of leaves of a Hamiltonian foliation and has a natural
groupoid structure. If it is a manifold then it is a symplectic groupoid for
the given Poisson manifold. We study various families of examples. In
particular, a global symplectic groupoid for a general class of two-dimensional
Poisson domains is constructed.Comment: 34 page
Coupling Poisson and Jacobi structures on foliated manifolds
Let M be a differentiable manifold endowed with a foliation F. A Poisson
structure P on M is F-coupling if the image of the annihilator of TF by the
sharp-morphism defined by P is a normal bundle of the foliation F. This notion
extends Sternberg's coupling symplectic form of a particle in a Yang-Mills
field. In the present paper we extend Vorobiev's theory of coupling Poisson
structures from fiber bundles to foliations and give simpler proofs of
Vorobiev's existence and equivalence theorems of coupling Poisson structures on
duals of kernels of transitive Lie algebroids over symplectic manifolds. Then
we discuss the extension of the coupling condition to Jacobi structures on
foliated manifolds.Comment: LateX, 38 page
Sur l'intégration symplectique de la structure de poisson singuliére Λ = (x2 + y2) ∂/∂x Λ ∂/∂y de R2
The purpose of this note is to give an example of a singular Poisson structure on R2 which admits a symplectic realization by a Lie groupoid
A Generalization of Poisson-Nijenhuis Structures
We generalize Poisson-Nijenhuis structures. We prove that on a manifold
endowed with a Nijenhuis tensor and a Jacobi structure which are compatible,
there is a hierarchy of pairwise compatible Jacobi structures.
Furthermore, we study the homogeneous Poisson-Nijenhuis structures and their
relations with Jacobi structures.Comment: 21 pages, Late
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