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Irreducible representations of a simple three-dimensional lie algebra over a field of finite characteristic

  • A. N. Rudakov
  • I. R. Shafarevich
Article

Abstract

The irreducible representations of a simple three-dimensional Lie algebra over a field of finite characteristic are enumerated. The dimensionalities of all representations do not exceed the characteristics p of the base field. For any dimensionality< p there exists a unique representation of this dimensionality. The representations of dimensionality p form a three-dimensional algebraic set. Six literature references are cited.

Keywords

Irreducible Representation Unique Representation Literature Reference Base Field Finite Characteristic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature cited

  1. 1.
    C. Curtis, Representations of Lie algebras of classical type with applications to linear groups, J. Math, and Mech.,9, 307–326 (1960).Google Scholar
  2. 2.
    H. Zassenhaus, The representations of Lie algebras of prime characteristic, Proc. Glasgow Math. Assoc.,2, 1–36 (1954).Google Scholar
  3. 3.
    A. Grothendieck, Fondements de la géométrie algébrique, Paris (1962) (preprint).Google Scholar
  4. 4.
    N. Jacobson, Lie Algebras [Russian translation], Moscow (1964).Google Scholar
  5. 5.
    N. Jacobson, Theory of Rings [Russian translation], Moscow (1947).Google Scholar
  6. 6.
    J. P. Serre, Coherent algebraic bundles, in Collection of translated articles entitled “Fiber Spaces and Their Applications” [Russian translation], Moscow (1958).Google Scholar

Copyright information

© Consultants Bureau 1968

Authors and Affiliations

  • A. N. Rudakov
    • 1
    • 2
  • I. R. Shafarevich
    • 1
    • 2
  1. 1.M. V. Lomonosov Moscow State UniversityUSSR
  2. 2.V. A. Steklov Mathematical InstituteAcademy of Sciences of the USSRUSSR

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