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On the Virasoro algebra as reduced Poisson submanifold of a Kac-Moody algebra on the circle


Author: Gloria Marí Beffa
Journal: Proc. Amer. Math. Soc. 122 (1994), 859-869
MSC: Primary 17B68; Secondary 22E65, 22E67, 58F07
MathSciNet review: 1204369
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Abstract: In this paper we show how the Lie-Poisson structure on the dual of the Virasoro algebra can be obtained through a standard Poisson reduction process performed on a Kac-Moody algebra on the circle. We use the geometrical idea of the process to establish some relation between transverse structures on both Poisson manifolds.


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DOI: https://doi.org/10.1090/S0002-9939-1994-1204369-7
Article copyright: © Copyright 1994 American Mathematical Society