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Dyson Boson-Fermion Realization of Lie (Super)Algebras

In: Symmetries in Science IX

Author

Listed:
  • D. V. Fursa

    (The Flinders University of South Australia, School of Physical Sciences)

  • Yu. F. Smirnov

    (U.N.A.M., Instituto de Ciencias Nucleares
    Institute for Nuclear Physics at Moscow State University)

  • V. N. Tolstoy

    (Moscow State University, Institute of Nuclear Physics)

Abstract

The aim of the present paper is to construct Dyson type [1, 2] boson-fermion realizations (BFR) of the arbitrary finite-dimensional contragredient Lie (super)algebra [3, 4] and to discuss how these realizations can be used to determine the matrix representations of (super)algebra. (Here we use the name “(super)algebra” in the following sense: It includes all semisimple finite-dimensional Lie algebras and all finite-dimensional contragredient Lie superalgebras.)

Suggested Citation

  • D. V. Fursa & Yu. F. Smirnov & V. N. Tolstoy, 1997. "Dyson Boson-Fermion Realization of Lie (Super)Algebras," Springer Books, in: Bruno Gruber & Michael Ramek (ed.), Symmetries in Science IX, pages 117-137, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-5921-4_9
    DOI: 10.1007/978-1-4615-5921-4_9
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