Spahn graded derivation (changes)

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If we have a graded algebra $A$, and $D$ is a homogeneous linear map of grade $d=|\mathrm{deg}(D<span><del\; class="diffmod">\; |</del><ins\; class="diffmod">\; )</ins></span>$ d = |D| deg(D) on $A$ then $D$ is a homogeneous derivation if

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

If the commutator factor$\epsilon = 1$ , this definition reduces to the usual Leibniz case. rule. 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.