Embedding of a Lie algebra into Lie-admissible algebras
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- by Hyo Chul Myung PDF
- Proc. Amer. Math. Soc. 73 (1979), 303-307 Request permission
Abstract:
Let A be a flexible Lie-admissible algebra over a field of characteristic $\ne$ 2, 3. Let S be a finite-dimensional classical Lie subalgebra of ${A^ - }$ which is complemented by an ideal R of ${A^ - }$. It is shown that S is a Lie algebra under the multiplication in A and is an ideal of A if and only if S contains a classical Cartan subalgebra H which is nil in A and such that $HH \subseteq S$ and $[H,R] = 0$. In this case, the multiplication between S and R is determined by linear functionals on R which vanish on [R, R]. If A is finite-dimensional and of characteristic 0 then this can be applied to give a condition that a Levi-factor S of ${A^ - }$ be embedded as an ideal into A and to determine the multiplication between S and the solvable radical of ${A^ - }$.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, 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
- Hyo Chul Myung, A subalgebra condition in Lie-admissible algebras, Proc. Amer. Math. Soc. 59 (1976), no. 1, 6–8. MR 422361, DOI 10.1090/S0002-9939-1976-0422361-6
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Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 73 (1979), 303-307
- MSC: Primary 17A30; Secondary 17A20
- DOI: https://doi.org/10.1090/S0002-9939-1979-0518509-8
- MathSciNet review: 518509