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{title2=$[\ell_m,\ell_n]=(m-n)\ell_{m+n}$}
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The Witt algebra is the <Lie algebra> of vector fields on a circle with Laurent-polynomial coefficients. Its nontrivial <central extension of a Lie algebra> is the <Virasoro algebra>.


Witt algebra

{title2=$0\to\mathfrak z\to\widehat{\mathfrak g}\to\mathfrak g\to0$}

= Lie algebra central extension
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A central extension is a <Lie algebra> surjection whose <kernel> commutes with every element of the larger algebra. The <Virasoro central extension> adds a central generator to the <Witt algebra>.


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 Incoming links: Central extension of a Lie algebra