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Infinite series of Lie algebras and boundary conditions for integrable systems

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Abstract

Representations of a quadratic R-matrix algebra in classical and quantum mechanics connected with Toda lattices associated with all infinite series of Lie algebras are constructed and studied. In particular, a new Lax representation for the Manakov top is presented. An so(2.1) dynamical algebra for the description of the adjoint Mathieu functions is given.

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Authors
  1. V. B. Kuznetsov
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  2. A. V. Tsyganov
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Akad. Nauk SSSR, Vol. 172, pp. 88–98, 1989.

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Kuznetsov, V.B., Tsyganov, A.V. Infinite series of Lie algebras and boundary conditions for integrable systems. J Math Sci 59, 1085–1092 (1992). https://doi.org/10.1007/BF01480690

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  • DOI: https://doi.org/10.1007/BF01480690

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