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Poisson-Nijenhuis Manifolds, Classical Yang-Baxter Equations, and Frobenius Algebras

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Classical and Quantum Physics

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 229))

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Abstract

In this paper we describe in detail the class of linear Poisson-Nijenhuis manifolds. We prove that they are related to Drinfeld’s bialgebras, classical Yang-Baxter equations, and noncommutative Frobenius algebras.

Dedicated to Alberto Ibort on the occasion of his 60th birthday.

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References

  1. A.A. Belavin, V.G. Drinfeld, Solutions of the classical Yang-Baxter equation for simple Lie algebras. Funct. Anal. Appl. 16, 1 (1982)

    Google Scholar 

  2. V.G. Drinfeld, Quantum groups, in Proceedings of the International Congress of Mathematicians (Berkeley, California, 1986), (Amer. Math. Soc, Providence, 1987), pp. 788–820

    Google Scholar 

  3. Y. Kosmann-Schwarzbach, F. Magri, Poisson-nijenhuis structures. Ann. Inst. Poincaré 53, 35–81 (1990)

    MathSciNet  MATH  Google Scholar 

  4. P. Libermann, C.-M. Marle, Symplectic Geometry and Analytical Mechanics (Reidel, Dordrecht, 1987)

    Book  Google Scholar 

  5. F. Magri, C. Morosi, A Geometrical Characterization of Integrable Hamiltonian Systems Through the Theory of Poisson–Nijenhuis Manifolds, Quaderno S19/1984 del Dip. di Matematica dell’Università di Milano (1984)

    Google Scholar 

  6. T. Marsico, Una caratterizzazione geometrica dei sistemi che ammettono la rappresentazione di Lax estesa, Ph.D. Thesis, Dip. di Matematica dell’Università di Milano (1996)

    Google Scholar 

  7. M.A. Semenov Tian Shansky, What is a classical R-matrix. Funct. Anal, Appl. 17, 259 (1983)

    Google Scholar 

  8. E.K. Sklyanin, Some algebraic structures connected with the Yang-Baxter equation. Funct. Anal. Appl. 16, 27 (1982)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica ed Applicazioni, Università di Milano Bicocca, Milan, Italy

    F. Magri

  2. Liceo Classico Berchet, Milan, Italy

    T. Marsico

Authors
  1. F. Magri
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  2. T. Marsico
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Corresponding author

Correspondence to F. Magri .

Editor information

Editors and Affiliations

  1. Università degli Studi di Napoli Federico II, Naples, Italy

    G. Marmo

  2. Institute of Mathematical Sciences (ICMAT), Madrid, Spain

    David Martín de Diego

  3. Universitat Politècnica de Catalunya, Barcelona, Spain

    Miguel Muñoz Lecanda

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Magri, F., Marsico, T. (2019). Poisson-Nijenhuis Manifolds, Classical Yang-Baxter Equations, and Frobenius Algebras. In: Marmo, G., Martín de Diego, D., Muñoz Lecanda, M. (eds) Classical and Quantum Physics. Springer Proceedings in Physics, vol 229. Springer, Cham. https://doi.org/10.1007/978-3-030-24748-5_15

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