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On the growth of almost soluble Lie algebras. (English) Zbl 1138.17304
Russ. Math. Surv. 60, No. 5, 970-972 (2005); translation from Usp. Mat. Nauk 60, No. 5, 165-166 (2005).
From the text: Using the notation and results from the second author’s previous papers, the purpose of the present note is the following subexponential upper estimate of the growth of almost soluble Lie algebras.
Theorem 2. Suppose that a finitely generated Lie algebra \(L\) has a subalgebra \(H\subseteq L\) of finite codimension which is soluble of derived length \(q\). Then \(\operatorname{Dim}^{q+1} L\leq \dim_K(L/ H)\).
MSC:
17B01 Identities, free Lie (super)algebras
17B30 Solvable, nilpotent (super)algebras
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