Supercommutative Algebra

A supercommutative algebra is a Z2 graded algebra such that for any two pure elements x,y of the algebra, yx=(-1)xyxy Equivalently, it is an algebra where the supercommutator
[x,y)≡xy-(-1)|x||y|yx
always vanishes. Grassmann algebras are examples of a supercommutative algebra. See also commutative algebra, Lie superalgebra

 

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