Poisson supermanifold

From Wikipedia, the free encyclopedia

A Poisson supermanifold is a differential supermanifold M such that the supercommutative algebra of smooth functions over it (let me clarify a bit. M isn't a point set space and so, doesn't "really" exist, and really, this algebra is all we have), is equipped with a bilinear map called the Poisson superbracket turning it into a Poisson superalgebra.

Every symplectic supermanifold is a Poisson supermanifold but not vice versa.

[edit] See also

• Poisson manifold
• Poisson algebra
• Poisson superalgebra
• noncommutative geometry