- Poisson superalgebra
In
mathematics , a Poisson superalgebra is a Z2-graded generalization of aPoisson algebra . Specifically, a Poisson superalgebra is an (associative)superalgebra "A" with aLie superbracket :such that ("A", [·,·] ) is aLie superalgebra and the operator:is asuperderivation of "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 algebra instead. This is used in theBRST andBatalin-Vilkovisky formalism.Examples
* 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.
ee also
*
Poisson supermanifold References
*springer|id=p/p110170|title=Poisson algebra|author=Y. Kosmann-Schwarzbach
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