2013/01/03 by Martin Schlichenmaier, Schlichenmaier, Martin
Mathematics · Physics and Astronomy · #17B56 (Primary) 17B68 #17B65 #17B66 #30F30 #81R10 #81T40 (Secondary) #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:17B56 #msc:17B65 #msc:17B66 #msc:17B68 #msc:30F30 #msc:81R10 #msc:81T40
paper · pdf · doi:10.48550/arxiv.1301.0484
23 pages, the revised version was prepared for final publication - only minor changes (language, typos etc.), change of title, correcting a reference
openalex publication_date 2013/01/03 · arxiv created 2013/03/25 · arxiv updated 2013/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Classically important examples of Lie superalgebras have been constructed starting from the Witt and Virasoro algebra. In this article we consider Lie superalgebras of Krichever-Novikov type. These algebras are multi-point and higher genus equivalents. The grading in the classical case is replaced by an almost-grading. The almost-grading is determined by a splitting of the set of points were poles are allowed into two disjoint subsets. With respect to a fixed splitting, or equivalently with respect to an almost-grading, it is shown that there is up to rescaling and equivalence a unique non-trivial central extension. It is given explicitly. Furthermore, a complete classification of bounded cocycles (with respect to the almost-grading) is given.