2001/12/12 by Martin Schlichenmaier, Schlichenmaier, Martin
Mathematics · Physics and Astronomy · #14H55 #17B56 #17B65 #17B66 #17B67 #30F30 #81R10 #81T40 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #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/0112116
38 pages, Amslatex, some minor changes in Section 7
openalex publication_date 2001/12/12 · arxiv created 2003/01/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Multi-point algebras of Krichever Novikov type for higher genus Riemann surfaces are generalisations of the Virasoro algebra and its related algebras. Complete existence and uniqueness results for local 2-cocycles defining almost-graded central extensions of the functions algebra, the vector field algebra, and the differential operator algebra (of degree ≤ 1) are shown. This is applied to the higher genus, multi-point affine algebras to obtain uniqueness for almost-graded central extensions of the current algebra of a simple finite-dimensional Lie algebra. An earlier conjecture of the author concerning the central extension of the differential operator algebra induced by the semi-infinite wedge representations is proved.