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Local cocycles and central extensions for multipoint algebras of Krichever-Novikov type. (English) Zbl 1124.17305
Summary: Multi-point algebras of Krichever-Novikov type for higher genus Riemann surfaces are generalisations of the Virasoro algebra and its related algebras. Complete existence and uniqueness results for local 2-cocycles defining almost-graded central extensions of the functions algebra, the vector field algebra, and the differential operator algebra (of degree \(\leq 1\)) are shown. This is applied to the higher genus, multi-point affine algebras to obtain uniqueness for almost-graded central extensions of the current algebra of a simple finite-dimensional Lie algebra. An earlier conjecture of the author concerning the central extension of the differential operator algebra induced by the semi-infinite wedge representations is proved.

MSC:
17B68 Virasoro and related algebras
17B66 Lie algebras of vector fields and related (super) algebras
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