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Hopf Algebras and Integrable Flows Related to the Heisenberg–Weil Coalgebra

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Ukrainian Mathematical Journal Aims and scope

Abstract

On the basis of the structure of Casimir elements associated with general Hopf algebras, we construct Liouville–Arnold integrable flows related to naturally induced Poisson structures on an arbitrary coalgebra and their deformations. Some interesting special cases, including coalgebra structures related to the oscillatory Heisenberg–Weil algebra and integrable Hamiltonian systems adjoint to them, are considered.

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Authors and Affiliations

  1. Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences, AGH University of Science and Technology, Krakow, Poland;, Lviv

    A. K. Prykarpatsky

  2. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    A. M. Samoilenko

  3. New Jersey Institute of Technology, Newark, New Jersey, USA

    D. L. Blackmore

Authors
  1. A. K. Prykarpatsky
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  2. A. M. Samoilenko
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  3. D. L. Blackmore
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Prykarpatsky, A.K., Samoilenko, A.M. & Blackmore, D.L. Hopf Algebras and Integrable Flows Related to the Heisenberg–Weil Coalgebra. Ukrainian Mathematical Journal 56, 109–121 (2004). https://doi.org/10.1023/B:UKMA.0000031706.91337.bd

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  • DOI: https://doi.org/10.1023/B:UKMA.0000031706.91337.bd

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