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VIDEO LIBRARY |
Scientific session of the Steklov Mathematical Institute dedicated to the results of 2014
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Lax operator algebras and gradings on semi-simple Lie algebras O. K. Sheinman |
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Abstract: Lax operator algebras are introduced in [1] in connection with the notion of Lax operator with spectral parameter on a Riemann surface (earlier introduced by I. M. Krichever). These are algebras of currents defined on Riemann surfaces and taking values in the semi-simple or reductive Lie algebras. They are closely related to integrable systems like Hitchin systems, Calogero–Moser systems, classical gyroscopes, problems of flow around a solid body. In many respects, the Lax operator algebras are analogous to the Kac–Moody algebras. Non-twisted Kac–Moody algebras are Lax operator algebras on Riemann sphere with marked points Up to the end of 2013 Lax operator algebras have been defined and constructed only for classical Lie algebras over References
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