= Affine current algebra
{title2=$[J_m^a,J_n^b]=if^{abc}J_{m+n}^c+km\delta_{m+n,0}\delta^{ab}$}
The affine current algebra is the one-dimensional central extension of the <loop algebra> of a finite-dimensional <Lie algebra>, with central element acting as the level $k$. A restricted module has $J_n v=0$ for all sufficiently large $n$ for each vector $v$; this makes the <Sugawara construction> finite on each vector after <normal ordering>. In a compact unitary positive-energy representation, the nontrivial integrable levels are positive integers in the standard basic normalization.
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