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This article is cited in 36 scientific papers (total in 36 papers)
Higher genus affine algebras of Krichever–Novikov type
M. Schlichenmaier University of Luxembourg
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.
Received: October 24, 2002
Citation:
M. Schlichenmaier, “Higher genus affine algebras of Krichever–Novikov type”, Mosc. Math. J., 3:4 (2003), 1395–1427
Linking options:
https://www.mathnet.ru/eng/mmj136 https://www.mathnet.ru/eng/mmj/v3/i4/p1395
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