Local cocycles and central extensions for multi-point algebras of Krichever-Novikov type

Martin Schlichenmaier

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arXiv · math/0112116

Local cocycles and central extensions for multi-point algebras of Krichever-Novikov type

Martin Schlichenmaier

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Abstract

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 \le 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.

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BibTeX RIS

Martin Schlichenmaier. 2003-01-02. Local cocycles and central extensions for multi-point algebras of Krichever-Novikov type. https://arxiv.org/abs/math/0112116

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