Abstract
Classically, starting from the Witt and Virasoro algebra important examples of Lie superalgebras were constructed. In this write-up of a talk presented at the Białowieża meetings we report on results on Lie superalgebras of Krichever–Novikov type. These algebras are multi-point and higher genus equivalents of the classical algebras. The grading in the classical case is replaced by an almost-grading. It is induced 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 a fixed almost-grading, it is shown that there is up to rescaling and equivalence a unique non-trivial central extension of the Lie superalgebra of Krichever–Novikov type. It is given explicitly.
Mathematics Subject Classification (2010). Primary: 17B56; Secondary: 17B68, 17B65, 17B66, 14H99, 81R10, 81T40.
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Schlichenmaier, M. (2015). Lie Superalgebras of Krichever–Novikov Type. In: Kielanowski, P., Bieliavsky, P., Odzijewicz, A., Schlichenmaier, M., Voronov, T. (eds) Geometric Methods in Physics. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-18212-4_16
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DOI: https://doi.org/10.1007/978-3-319-18212-4_16
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-18211-7
Online ISBN: 978-3-319-18212-4
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