Poissongeometriassa
Poisson geometry is a field of mathematics that studies Poisson manifolds. A Poisson manifold is a differentiable manifold equipped with a Poisson bracket, which is a bilinear operation on the algebra of smooth functions on the manifold that satisfies certain properties. The Poisson bracket defines a Lie algebra structure on the space of smooth functions and also allows for the definition of Hamiltonian vector fields.
The concept of Poisson geometry arises naturally in Hamiltonian mechanics and symplectic geometry. Symplectic manifolds are
Key objects in Poisson geometry include Poisson algebras, which are commutative algebras equipped with a Poisson
Research in Poisson geometry explores topics such as deformation quantization, which quantizes Poisson manifolds, and the