Higher genus affine algebras of Krichever - Novikov type

Details Higher genus affine algebras of Krichever - Novikov type Higher genus affine algebras of Krichever - Novikov type

2002-10-23

arxiv.org/abs/math/0210360v2

Mathematics

Quantum Algebra

35 pages

Scientific paper

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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