Poisson supermanifold

In differential geometry a Poisson supermanifold is a differential supermanifold M such that the supercommutative algebra of smooth functions over it (to clarify this: M is not a point set space and so, doesn't "really" exist, and really, this algebra is all we have), $C^\infty(M)$ 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.

See also

• Poisson manifold
• Poisson algebra
• Noncommutative geometry