A characterization of $p$-reductive Lie algebras
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- by Robert Lee Wilson
- Proc. Amer. Math. Soc. 32 (1972), 89-90
- DOI: https://doi.org/10.1090/S0002-9939-1972-0291238-8
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Abstract:
Let $\mathfrak {L}$ be a finite dimensional restricted Lie algebra over a field of characteristic $p > 0$. Then $\mathfrak {L}$ has a completely reducible faithful finite dimensional restricted representation if and only if $\mathfrak {L}$ has no nonzero nil ideals.References
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- Nathan Jacobson, Rational methods in the theory of Lie algebras, Ann. of Math. (2) 36 (1935), no.Ā 4, 875ā€“881. MR 1503258, DOI 10.2307/1968593
- N. Jacobson, A note on Lie algebras of characteristic $p$, Amer. J. Math. 74 (1952), 357ā€“359. MR 47026, DOI 10.2307/2372000
- G. B. Seligman, Modular Lie algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 40, Springer-Verlag New York, Inc., New York, 1967. MR 0245627
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 32 (1972), 89-90
- MSC: Primary 17B20
- DOI: https://doi.org/10.1090/S0002-9939-1972-0291238-8
- MathSciNet review: 0291238