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Super Hamiltonian Operators and Lie Superalgebras

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Nonlinear Evolution Equations and Dynamical Systems

Part of the book series: Research Reports in Physics ((RESREPORTS))

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Abstract

A superversion of the formal calculus of variations as developed by I.M. Gel’fand et al. is presented. It is proved that with a linear super Hamiltonian operator one can associate a Lie superalgebra structure on the space of (reduced) 1-forms and vice versa. Also a theorem is proved about the connection between cocycles on this Lie superalgebra and super Hamiltonian operators. Finally an application is given.

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References

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Author information

Authors and Affiliations

  1. Mathematical Institute, University of Amsterdam, Plantage Muidergracht 24, 1018 TV, Amsterdam, The Netherlands

    E. D. van der Lende & H. G. J. Pijls

Authors
  1. E. D. van der Lende
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  2. H. G. J. Pijls
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Editor information

Editors and Affiliations

  1. Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università di Roma „La Sapienza“, via A. Scarpa 10, I-00161, Roma, Italy

    Sandra Carillo

  2. Dipartimento di Fisica, Università di Roma „La Sapienza“, P. le A. Moro 2, I-00185, Roma, Italy

    Orlando Ragnisco

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© 1990 Springer-Verlag Berlin, Heidelberg

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van der Lende, E.D., Pijls, H.G.J. (1990). Super Hamiltonian Operators and Lie Superalgebras. In: Carillo, S., Ragnisco, O. (eds) Nonlinear Evolution Equations and Dynamical Systems. Research Reports in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84039-5_31

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  • DOI: https://doi.org/10.1007/978-3-642-84039-5_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51983-6

  • Online ISBN: 978-3-642-84039-5

  • eBook Packages: Springer Book Archive

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