Structure Theory for One Class of Locally Finite Lie Algebras

الأصل · EN

In this paper I consider locally finite Lie algebras of characteristic zero satisfying the condition that for every finite number of elements x₁, x₂,..., xₖ of such an algebra L there is finite-dimensional subalgebra A which contains these elements and L(adA)ⁿ⊂ 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.