= Gerstenhaber bracket
{c}
{title2=$[f,g]$}
Write $f\circ g=\sum_{i=0}^{p-1}(-1)^{i(q-1)}f\circ_i g$ for insertion of a degree-$q$ cochain into a degree-$p$ one. With the unsigned <Hochschild cup product> and the left <graded Leibniz rule>, take $[f,g]=(-1)^{(p-1)(q-1)}f\circ g-g\circ f$. It descends to <Hochschild cohomology> and gives a <Gerstenhaber algebra>. The alternative insertion bracket $f\circ g-(-1)^{(p-1)(q-1)}g\circ f$ differs by the displayed degree sign and obeys the corresponding right rule. Degree-one brackets are <commutators> of <derivations> in either convention.
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