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Two Types of Poisson Pencils and Related Quantum Objects

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Lie Groups and Lie Algebras

Part of the book series: Mathematics and Its Applications ((MAIA,volume 433))

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Abstract

Two types of Poisson pencils connected to classical R-matrices and their quantum counterparts are considered. A representation theory of the quantum algebras related to some symmetric orbits in sl(n)* is constructed. A twisted version of quantum mechanics is discussed.

Mathematics Subject Classification (1991): 17B37, 81R50.

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Author information

Authors and Affiliations

  1. ISTV, Université de Valenciennes, 59304, Valenciennes, France

    D. Gurevich

  2. Department of Mathematics, Bar-Ilan University, 52900, Ramat-Gan, Israel

    J. Donin

  3. ITEP, Bol Tcheremushkinskaya 25, 117259, Moscow, Russia

    V. Rubtsov

Authors
  1. D. Gurevich
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  2. J. Donin
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  3. V. Rubtsov
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Editor information

Editors and Affiliations

  1. International Sophus Lie Center, Minsk, Belarus

    B. P. Komrakov

  2. Moscow Institute for Municipal Economy and Diffiety Institute, Moscow, Russia

    I. S. Krasil’shchik

  3. Institute for New Technologies, Moscow, Russia

    G. L. Litvinov

  4. Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

    A. B. Sossinsky

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© 1998 Springer Science+Business Media Dordrecht

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Gurevich, D., Donin, J., Rubtsov, V. (1998). Two Types of Poisson Pencils and Related Quantum Objects. In: Komrakov, B.P., Krasil’shchik, I.S., Litvinov, G.L., Sossinsky, A.B. (eds) Lie Groups and Lie Algebras. Mathematics and Its Applications, vol 433. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5258-7_3

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  • DOI: https://doi.org/10.1007/978-94-011-5258-7_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6212-1

  • Online ISBN: 978-94-011-5258-7

  • eBook Packages: Springer Book Archive

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