Editing Lie superalgebra (section)

== Comments == 
Lie superalgebras show up in physics in several different ways. In conventional [[supersymmetry]], the ''even'' elements of the superalgebra correspond to [[boson]]s and ''odd'' elements to [[fermion]]s. This corresponds to a bracket that has a grading of zero:
:<math>|[a,b]| = |a|+|b|</math>

This is not always the case; for example, in [[BRST supersymmetry]] and in the [[Batalin–Vilkovisky formalism]], it is the other way around, which corresponds to the bracket of having a grading of -1: 
:<math>|[a,b]| = |a|+|b|-1</math>

This distinction becomes particularly relevant when an algebra has not one, but two [[graded ring|graded associative products]]. In addition to the Lie bracket, there may also be an "ordinary" product, thus giving rise to the [[Poisson superalgebra]] and the [[Gerstenhaber algebra]]. Such gradings are also observed in [[deformation theory]].