Structure Theory for One Class of Locally Finite Lie Algebras

Details Structure Theory for One Class of Locally Finite Lie Algebras Structure Theory for One Class of Locally Finite Lie Algebras

2003-10-14

arxiv.org/abs/math/0310208v1

Mathematics

Rings and Algebras

Scientific paper

In this paper I consider locally finite Lie algebras of characteristic zero satisfying the condition that for every finite number of elements $x_{1}, x_{2},..., x_{k}$ of such an algebra $L$ there is finite-dimensional subalgebra $A$ which contains these elements and $L(adA)^n\subset A$ for some integer $n$. For such algebras I prove several structure theorems that can be regarded as generalizations of the classical structure theorems of the finite-dimensional Lie algebras theory.

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