Infinitesimal Takesaki duality of Hamiltonian vector fields on a symplectic manifold File “take.tex “/dir paper/deformation /Takesaki Infinitesimal Takesaki duality of Hamiltonian vector fields on a symplectic manifold
نویسنده
چکیده
For an infinitesimal symplectic action of a Lie algebra g on a symplectic manifold, we construct an infinitesimal crossed product of Hamiltonian vector fields and Lie algebra g. We obtain its second crossed product in case g = R and show an infinitesimal version for a theorem type of Takesaki duality.
منابع مشابه
Infinitesimal Takesaki duality of Hamiltonian vector fields on a symplectic manifold
For an infinitesimal symplectic action of a Lie algebra g on a symplectic manifold, we construct an infinitesimal crossed product of Hamiltonian vector fields and Lie algebra g. We obtain its second crossed product in case g = R and show an infinitesimal version for a theorem type of Takesaki duality.
متن کاملLifts of Poisson and Related Structures
The derivation d T on the exterior algebra of forms on a manifold M with values in the exterior algebra of forms on the tangent bundle T M is extended to multivector fields. These tangent lifts are studied with applications to the theory of Poisson structures, their symplectic foliations, canonical vector fields and Poisson-Lie groups. 0. Introduction. A derivation d T on the exterior algebra o...
متن کاملL∞-algebras of Local Observables from Higher Prequantum Bundles
To any manifold equipped with a higher degree closed form, one can associate an L∞-algebra of local observables that generalizes the Poisson algebra of a symplectic manifold. Here, by means of an explicit homotopy equivalence, we interpret this L∞-algebra in terms of infinitesimal autoequivalences of higher prequantum bundles. By truncating the connection data on the prequantum bundle, we produ...
متن کاملGENERALIZED SYMPLECTIC GEOMETRY ON THE FRAME BUNDLE OF A MANIFOLD† by
In this paper we develope the fundamentals of the generalized symplectic geometry on the bundle of linear frames LM of an n-dimensional manifold M that follows upon taking the R-valued soldering 1-form θ on LM as a generalized symplectic potential. The development is centered around generalizations of the basic structure equation df = −Xf ω of standard symplectic geometry to LM when the symplec...
متن کاملHamiltonian Stationary Tori in the Complex Projective Plane
Hamiltonian stationary Lagrangian surfaces are Lagrangian surfaces of a given four-dimensional manifold endowed with a symplectic and a Riemannian structure, which are critical points of the area functional with respect to a particular class of infinitesimal variations preserving the Lagrangian constraint: the compactly supported Hamiltonian vector fields. The Euler–Lagrange equations of this v...
متن کامل