2002/10/23 by Martin Schlichenmaier, Schlichenmaier, Martin
Mathematics · Physics and Astronomy · #14H55 #17B56 #17B65 #17B66 #17B67 #30F30 #81R10 #81T40 #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math-ph #math.AG #math.MP #math.QA #math.RA #msc:14H55 #msc:17B56 #msc:17B65 #msc:17B66 #msc:17B67 #msc:30F30 #msc:81R10 #msc:81T40
paper · pdf · doi:10.48550/arxiv.math/0210360
35 pages
arxiv created 2003/01/02 · arxiv updated 2009/11/30
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.