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 algebras.
Key words and phrases:Krichever–Novikov algebras, central extensions, almost-grading, conformal field theory, infinite-dimensional Lie algebras, affine algebras, differential operator algebras, local cocycles.
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