- Poisson superalgebra
mathematics, a Poisson superalgebra is a Z2-graded generalization of a Poisson algebra. Specifically, a Poisson superalgebra is an (associative) superalgebra"A" with a Lie superbracket:such that ("A", [·,·] ) is a Lie superalgebraand the operator:is a superderivationof "A"::
A supercommutative Poisson algebra is one for which the (associative) product is supercommutative.
This is one possible way of "super"izing the Poisson algebra. This gives the classical dynamics of fermion fields and classical spin-1/2 particles. The other is to define an
antibracket algebrainstead. This is used in the BRSTand Batalin-Vilkoviskyformalism.
* If "A" is any associative Z2 graded algebra, then, defining a new product [.,.] by [x,y] =xy-(-1)|x||y|yx for any pure graded x, y turns "A" into a Poisson superalgebra.
*springer|id=p/p110170|title=Poisson algebra|author=Y. Kosmann-Schwarzbach
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