Abstract
Let $M$ be a paracompact smooth manifold, $A$ a Weil algebra and $M^{A}$ theassociated Weil bundle. In this paper, we give a characterization ofhamiltonian field on $M^{A}$ in the case of Poisson manifold and ofSymplectic manifold.
Highlights
In what follows, we denote M, a paracompact differentiable manifold of dimension n, C∞(M) the algebra of smooth functions on M and A a local algebra in the sense of Andre Weil i.e a real commutative algebra of finite dimension, with unit, and with an unique maximal ideal m of codimension 1 over R[14]
We recall that a near point of x ∈ M of kind A is a morphism of algebras ξ : C∞(M) −→ A
Such that ξ( f ) − f (x) ∈ m for any f ∈ C∞(M)
Summary
We denote M, a paracompact differentiable manifold of dimension n, C∞(M) the algebra of smooth functions on M and A a local algebra in the sense of Andre Weil i.e a real commutative algebra of finite dimension, with unit, and with an unique maximal ideal m of codimension 1 over R[14]. In this case, there exists an integer h such that mh+1 = (0) and mh (0). X(M) −→ DerA[C∞(MA, A)], θ −→ θA is an injective morphism of R-Lie algebras
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