**Journal of Lie Theory
**

Vol. 9, No. 1, pp. 125-156 (1999)

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On the classification of metabelian Lie algebras

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L. Yu. Galitzki, D. A. Timashev

Philippinenhöfer Weg, 26

Kassel, 34127, Deutschland

Chair of Algebra

Department of Mathematics

Moscow State University

Moscow, 119899, Russia

timashev@mech.math.msu.su

**Abstract:** We classify metabelian Lie algebras with successive dimensions of quotients of the lower central series ${\scriptstyle(m,n)=(5,5)}$ and ${\scriptstyle(6,3)}$. The problem is reduced to describing orbits of the linear group ${\scriptstyle \Ext^2\SL_m\otimes\SL_n}$, the latter being a ${\scriptstyle\theta}$-group in both cases. The results obtained in the paper allow to complete the classification of metabelian Lie algebras of dimension up to ${\scriptstyle 9}$.

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