A subalgebra condition in Lie-admissible algebras
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- by Hyo Chul Myung PDF
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Abstract:
Let $A$ be a finite-dimensional, flexible, Lie-admissible algebra over a field $\Phi$ of characteristic $\ne 2$. Let $S$ be a subalgebra of ${A^ - }$ and $H$ be a Cartan subalgebra of $S$. It is shown that $S$ is a subalgebra of $A$ if and only if $HH \subseteq S$.References
- P. J. Laufer and M. L. Tomber, Some Lie admissible algebras, Canadian J. Math. 14 (1962), 287–292. MR 136636, DOI 10.4153/CJM-1962-020-9
- Hyo Chul Myung, A remark on the proof of a theorem of Laufer and Tomber, Canadian J. Math. 23 (1971), 270. MR 269707, DOI 10.4153/CJM-1971-026-1
- Hyo Chul Myung, Some classes of flexible Lie-admissible algebras, Trans. Amer. Math. Soc. 167 (1972), 79–88. MR 294419, DOI 10.1090/S0002-9947-1972-0294419-7
- G. B. Seligman, Modular Lie algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 40, Springer-Verlag New York, Inc., New York, 1967. MR 0245627
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 59 (1976), 6-8
- MSC: Primary 17A20
- DOI: https://doi.org/10.1090/S0002-9939-1976-0422361-6
- MathSciNet review: 0422361