graded derivation (Rev #1, changes)

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If we have a graded algebra $A$, and $D$ is a homogeneous linear map of grade $d = |D|$ on $A$ then $D$ is a homogeneous derivation if

$D(ab)=D(a)b+\epsilon^{|a||D|}aD(b)$

$\epsilon\in\{-1,1\}$ acting on homogeneous elements of $A$. A graded derivation is sum of homogeneous derivations with the same $\epsilon$.

If the commutator factor $\epsilon = 1$, this definition reduces to the usual case. If $\epsilon = -1$, however, then $D(ab)=D(a)b+(-1)^{|a|}aD(b)$, for odd $|D|$. They are called anti-derivations.

Examples of anti-derivations include the exterior derivative? and the interior product? acting on differential form?s.