Cartan subalgebras and tori in prime characteristic
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- by Robert Lee Wilson PDF
- Proc. Amer. Math. Soc. 53 (1975), 325-327 Request permission
Abstract:
Let $L$ be a finite dimensional (not necessarily restricted) Lie algebra over a perfect field $F$ of characteristic $p > 0$. Let $\overline L$ be any finite dimensional restricted Lie algebra containing $L$. The Cartan subalgebras of $L$ are characterized as the centralizers of certain tori in $\overline L$.References
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S. Demuškin, Cartan subalgebras of the simple Lie $p$-algebras ${W_n}$ and ${S_n}$, Sibirsk. Mat. Ž. 11 (1970), 310-324 = Siberian Math. J. 11 (1970), 233-245. MR 41 #6919.
- S. P. Demuškin, Cartan subalgebras of simple non-classical Lie $p$-algebras, Izv. Akad. Nauk SSSR Ser. Mat. 36 (1972), 915–932 (Russian). MR 0327854
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- John R. Schue, Cartan decompositions for Lie algebras of prime characteristic, J. Algebra 11 (1969), 25–52. MR 231873, DOI 10.1016/0021-8693(69)90099-4
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 325-327
- MSC: Primary 17B05
- DOI: https://doi.org/10.1090/S0002-9939-1975-0384886-0
- MathSciNet review: 0384886