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Irreducible representations of a simple three-dimensional Lie algebra over a field of finite characteristic. (English. Russian original) Zbl 0184.06002

Math. Notes 2, No. 5, 760-767 (1967); translation from Mat. Zametki 2, No. 5, 439-454 (1967).
Summary: 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.

MSC:

17B50 Modular Lie (super)algebras
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
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