Abstract
In this paper, M is a smooth manifold of finite dimension n, A is a local algebra and MA is the associated Weil bundle. We study Poisson vector fields on MA and we prove that all globally hamiltonian vector fields on MA are Poisson vector fields.
Highlights
In what follows we denote by A a Weil algebra, M a smooth manifold, C∞ ( M ) the algebra of smooth functions on M
A near point of x ∈ M of kind A is a homomorphism of algebras ξ :C∞ (M ) → A
( ) ( ) i.e. X is the interior derivation of the Poisson A-algebra C∞ M A, A [6]
Summary
In what follows we denote by A a Weil algebra, M a smooth manifold, C∞ ( M ) the algebra of smooth functions on M. ( ) ( ) We denote X M A , the set of vector fields on M A and DerA C∞ M A , A the set of A-linear maps ( ) ( ) X : C∞ M A , A → C∞ M A , A Is a vector field on M, there exists one and only one A-linear derivation
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