We introduce a natural class of multicomponent local Poisson structures $$\mathcal P_k + \mathcal P_1$$ , where is bracket order one and P_k$$ homogeneous odd $$k$$ under the assumption that has Darboux coordinates (Darboux–Poisson bracket) nondegenerate. For such brackets, we obtain general formulas in arbitrary coordinates, find normal forms (related to Frobenius triples), provide description...

There are also four appendices. Let K be a field of characteristic 0, and let C be a commutative K-algebra. which makes C into a Lie algebra, and is a biderivation (i.e. a derivation in each argument). The pair C, {−, −} is called a Poisson algebra. Poisson brackets arise in several ways. Example 1.1. Classical Hamiltonian mechanics. Here K = R, X is an even dimensional differentiable manifold ...

We obtain Hamilton equations for the gravitational field and demonstrate the conservation of total energy. We derive the Poisson bracket equation for a general dynamical variable.

In this paper we relate the geometric Poisson brackets on the 2Grassmannian in R4 and on the (2, 2) Möbius sphere. We show that, when written in terms of local moving frames, the geometric Poisson bracket on the Möbius sphere does not restrict to the space of differential invariants of Schwarzian type. But when the concept of conformal natural frame is transported from the conformal sphere into...

We relate the machinery of persistence modules to Legendrian contact homology theory and Poisson bracket invariants, use it show existence connecting trajectories symplectic Hamiltonian flows.

It is well known that free (unconstrained) initial data for the gravitational field in general relativity can be identified on an initial hypersurface consisting of two intersecting null hypersurfaces. Here the phase space of vacuum general relativity associated with such an initial data hypersurface is defined; a Poisson bracket is defined, via Peierls’ prescription, on sufficiently regular fu...

In this paper, we compute the Gerstenhaber bracket on the Hochschild cohomology of C∞(M)⋊Γ. Using this computation, we classify all the noncommutative Poisson structures on C∞(M) ⋊ Γ when M is a symplectic manifold. We provide examples of deformation quantizations of these noncommutative Poisson structures.

Alan Weinstein office 825 Evans 642-3518 [email protected] OH: T 9:40-11, R 12:40-2 math.berkeley.edu/~alanw bspace.berkeley.edu GSI(sorta):Christian Bloman? orbit method in representation theory. symplectic geometry and algebraic geometry. moment maps. Attiya. 90s. conformal field theory. Syberg-Witten theory. Poisson bracket ... lie algebra structure. Leads to Poisson geometry. Mechanic...

The problem treated here is to find the Hamiltonian structure for an ideal gauge-charged fluid. Using a Kaluza-Klein point of view, we obtain the non-canonical Poisson bracket and the motion equations by a Poisson reduction involving the automorphism group of a principal bundle.

In this paper, we compute the Gerstenhaber bracket on the Hochschild cohomology of C∞(M)⋊Γ. Using this computation, we classify all the noncommutative Poisson structures on C∞(M) ⋊ Γ when M is a symplectic manifold. We provide examples of deformation quantizations of these noncommutative Poisson structures.