Ukrainian Mathematical Journal

, Volume 56, Issue 1, pp 109–121 | Cite as

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

  • A. K. Prykarpatsky
  • A. M. Samoilenko
  • D. L. Blackmore


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.


Hamiltonian System Hopf Algebra Poisson Structure Flow Relate Integrable Hamiltonian System 
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Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • A. K. Prykarpatsky
    • 1
  • A. M. Samoilenko
    • 2
  • D. L. Blackmore
    • 3
  1. 1.Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of SciencesAGH University of Science and Technology, Krakow, Poland;Lviv
  2. 2.Institute of MathematicsUkrainian Academy of SciencesKiev
  3. 3.New Jersey Institute of TechnologyNewarkUSA

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