= Lie algebra two-cocycle
{c}
{title2=$\kappa\in\Lambda^2\mathfrak g^*$}
For trivial real coefficients, a Lie algebra two-cocycle is an alternating bilinear form satisfying $\kappa([X,Y],Z)+\kappa([Y,Z],X)+\kappa([Z,X],Y)=0$. Adding a form $b([X,Y])$ does not change its <Lie algebra cohomology> class. The bracket $[(X,a),(Y,b)]=([X,Y],\kappa(X,Y))$ defines a <central extension of a Lie algebra> by $\mathbb R$ precisely when this cocycle identity holds. The constant discrepancy in a <moment-map equivariance obstruction> is such a cocycle.
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