Lie algebras represented as a sum of two subalgebras

Research Report MRR98-065

Lie algebras represented as a sum of two subalgebras

Masanobu Honda and Takanori Sakamoto

Abstract: Let L be a Lie algebra represented as a sum of two subalgebras A and B. We prove that if L belongs to a subclass of the class of locally finite Lie algebras over a field of characteristic $\neq 2$ and both A and B are locally nilpotent, then L is locally soluble. We also prove that if L is a serially finite Lie algebra over a field of characteristic zero, then any common serial subalgebra of A and B is serial in L.

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Download paper:	gzipped DVI file (34K)

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	DVI file (2K)