Poisson superalgebra
In mathematics, a Poisson superalgebra is a Z2-graded generalization of a Poisson algebra. Specifically, a Poisson superalgebra is an superalgebra A with a Lie superbracket
such that is a Lie superalgebra and the operator
is a superderivation of A:
A supercommutative Poisson algebra is one for which the 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 the BRST and Batalin-Vilkovisky formalism.Examples
