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Continual Lie algebra bicomplexes and integrable models

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Abstract

We introduce bicomplex structures associated with Saveliev-Vershik continual Lie algebras, and derive non-linear dynamical systems resulting from the bicomplex conditions. Examples related to classes of continual Lie algebras, including contact Lie, Poisson bracket, and Hilbert-Cartan ones are discussed. Using the bicomplex linearization problem, we derive corresponding conservation laws.

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References

  1. A. Dimakis and F. Muller-Hoissen: Int. J. Mod. Phys. B 14 (2000) 2455; hep-th/0006005.

    MathSciNet  ADS  Google Scholar 

  2. E.P. Gueuvoghlanian: J. Phys. A: Math. Gen. 34 (2001) L425; hep-th/0105015.

    Article  MathSciNet  MATH  ADS  Google Scholar 

  3. A.N. Leznov and M.V. Saveliev: Group-theoretical methods for integration of nonlinear dynamical systems. Progress in Physics Series, Vol. 15, Birkhauser-Verlag, Basel, 1992.

    Google Scholar 

  4. I. Bakas: hep-th/0410093.

  5. H.-D. Cao and B. Chow: Bull. Am. Math. Soc. 36 (1999) 59; math.DG/9811123. G. Perelman: math.DG/0211159.

    Article  MathSciNet  Google Scholar 

  6. A. Zuevsky: Vertex operator solutions to Ricci flow equation. In preparation.

  7. M.V. Saveliev and A.M. Vershik: Commun. Math. Phys. 126 (1989) 367. M.V. Saveliev and A.M. Vershik: Phys. Lett. A 143 (1990) 121. R.M. Kashaev, M.V. Saveliev, S.A. Savelieva, and A.M. Vershik: in Ideas and methods in mathematical analysis, stochastics, and applications, Oslo, 1988 (Eds. S. Albeverio, J.E. Fenstad, H. Holden, and T. Lindstrom), Cambridge Univ. Press, Cambridge, 1992, p. 295.

    Article  MathSciNet  Google Scholar 

  8. D.B. Fuks: Cohomology of infinite-dimensional Lie algebras. Contemporary Soviet Mathematics, Consultants Bureau, New York, 1986.

    Google Scholar 

  9. M.V. Saveliev: LPTENS-93/43; hep-th/9311035.

  10. A. Zuevsky: Higher grading continual Lie algebra bicomplexes and associated integrable models. In preparation.

  11. L.A. Ferreira, J-L. Gervais, J. Sanchez Guillen, and M.V. Saveliev: Nucl. Phys. B 470 (1996) 236; hep-th/9512105.

    Article  MathSciNet  ADS  Google Scholar 

  12. A. Zuevsky: Czech J. Phys. 54 (2004) 501; J. Phys. A: Math. Gen. 37 (2004) 537.

    MathSciNet  Google Scholar 

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  1. Max-Planck Institute fur Mathematik, Vivatsgasse 7, 53111, Bonn, Germany

    A. Zuevsky

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  1. A. Zuevsky
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Zuevsky, A. Continual Lie algebra bicomplexes and integrable models. Czech J Phys 55, 1545–1551 (2005). https://doi.org/10.1007/s10582-006-0039-0

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  • DOI: https://doi.org/10.1007/s10582-006-0039-0

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