Editing Poisson algebra (section)

===Z<sub>2</sub> grading===
Poisson algebras can be given a '''Z'''<sub>2</sub>-[[graded algebra|grading]] in one of two different ways. These two result in the [[Poisson superalgebra]] and the [[Gerstenhaber algebra]]. The difference between the two is in the grading of the product itself. For the Poisson superalgebra, the grading is given by
:<math>|\{a,b\}| = |a|+|b|</math>
whereas in the Gerstenhaber algebra, the bracket decreases the grading by one:
:<math>|\{a,b\}| = |a|+|b| - 1</math>

In both of these expressions <math>|a|=\deg a</math> denotes the grading of the element <math>a</math>; typically, it counts how <math>a</math> can be decomposed into an even or odd product of generating elements. Gerstenhaber algebras conventionally occur in [[BRST quantization]].