Supercommutative Algebra
A
supercommutative algebra
is a
Z
2
graded algebra
such that for any two
pure elements
x,y of the
algebra
, yx=(-1)
xy
xy 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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