Poisson supermanifold

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), C^infty(M) is equipped with a bilinear map called the Poisson superbracket turning it into a Poisson superalgebra.

Related Topics:
Supermanifold - Supercommutative algebra - Smooth function - Bilinear map - Poisson superbracket - Poisson superalgebra

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

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See also Poisson manifold, Poisson algebra, Poisson superalgebra, noncommutative geometry

Related Topics:
Poisson manifold - Poisson algebra - Poisson superalgebra - Noncommutative geometry

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