Embedding of a lie algebra into lie-admissible algebras
Cartan subalgebra, Classical Lie algebra, Flexible algebra, Levi-factor, Lie-admissible algebra
Proceedings of the American Mathematical Society
Let A be a flexible Lie-admissible algebra over a field of characteristic ≠ 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 5 contains a classical Cartan subalgebra H which is nil in A and such that HH ⊂ S and [H, R] = 0. In this case, the multiplication between S and R is determined by linear functional 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¯. © 1979 American Mathematical Society.
Original Publication Date
DOI of published version
Myung, Hyo Chul, "Embedding of a lie algebra into lie-admissible algebras" (1979). Faculty Publications. 4983.