Graded Leibniz rule
= Graded Leibniz rule
{title2=$L(ab)=L(a)b+(-1)^{r|a|}aL(b)$}
On a <graded algebra>, a left derivation of degree $r$ satisfies the displayed rule for homogeneous $a$. A right derivation of degree $r$ satisfies $R(ab)=aR(b)+(-1)^{r|b|}R(a)b$. For odd $r$, these reduce to the familiar parity sign rules. The left <Gerstenhaber bracket> makes $[u,-]$ a left derivation of degree $|u|-1$ on <Hochschild cohomology>; this rule holds for the induced <cohomology> operations, not necessarily for their cochain representatives.