= Second-order obstruction to an associative deformation
{title2=$\delta\mu_2=f(f(a,b),c)-f(a,f(b,c))$}
Expanding <associativity> for $a*b=ab+tf(a,b)+t^2\mu_2(a,b)$ modulo $t^3$ gives the displayed equation. If $\delta f=0$, its right side is a degree-three <Hochschild cocycle>. Its class in $HH^3(R,R)$ must vanish to extend the first-order <formal associative deformation> to second order. A nonzero class in $HH^2$ therefore need not integrate to a full <formal associative deformation>.
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