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Higher genus affine algebras of Krichever - Novikov type

Martin Schlichenmaier
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Abstract

For higher genus multi-point current algebras of Krichever-Novikov type associated to a finite-dimensional Lie algebra, local Lie algebra two-cocycles are studied. They yield as central extensions almost-graded higher genus affine Lie algebras. In case that the Lie algebra is reductive a complete classification is given. For a simple Lie algebra, like in the classical situation, there is up to equivalence and rescaling only one non-trivial almost-graded central extension. The classification is extended to the algebras of meromorphic differential operators of order less or equal one on the currents algebra.

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Martin Schlichenmaier. 2003-01-02. Higher genus affine algebras of Krichever - Novikov type. https://arxiv.org/abs/math/0210360

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