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Title

SOME CHARACTERIZATIONS OF SOLVABLE LIE ALGEBRAS

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Abstract

 FOR A PROPER SUBALGEBRA K OF A LIE ALGEBRA L, A PAIR (A,B) OF SUBALGEBRAS OF L IS CALLED A Q-PAIR IF L = ÁA,KÑ, B IS THE LARGEST IDEAL OF L CONTAINED IN A ∩ K AND FOR EACH PROPER SUBALGEBRA C/B OF A/B WHICH IS AN IDEAL OF L/B, WE HAVE L ¹ C + K. IN THIS ARTICLE, WE STUDY THE Q-PAIRS FOR 2-MAXIMAL SUBALGEBRAS OF A LIE ALGEBRA, WHICH IMPLY A FINITE DIMENSIONAL LIE ALGEBRA TO BE SOLVABLE.

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