The second Lie algebra cohomology of the d-dimensional Witt algebra is computed for all d>2, giving a complete classification of central extensions, and a local universal Grothendieck-Riemann-Roch theorem is proved.
Two-dimensional Virasoro algebras
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abstract
We classify central extensions of the dg Lie algebra of derived global sections of the tangent sheaf on the punctured, formal 2-disk. We then prove a local and universal form of the Grothendieck--Rieman--Roch theorem for families of two-dimensional complex varieties.
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Higher-dimensional Virasoro algebras
The second Lie algebra cohomology of the d-dimensional Witt algebra is computed for all d>2, giving a complete classification of central extensions, and a local universal Grothendieck-Riemann-Roch theorem is proved.