Concept

Poisson supermanifold

Summary
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
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