Czechoslovak Mathematical Journal

, Volume 63, Issue 3, pp 847–863 | Cite as

The classification of two step nilpotent complex Lie algebras of dimension 8



A Lie algebra g is called two step nilpotent if g is not abelian and [g, g] lies in the center of g. Two step nilpotent Lie algebras are useful in the study of some geometric problems, such as commutative Riemannian manifolds, weakly symmetric Riemannian manifolds, homogeneous Einstein manifolds, etc. Moreover, the classification of two-step nilpotent Lie algebras has been an important problem in Lie theory. In this paper, we study two step nilpotent indecomposable Lie algebras of dimension 8 over the field of complex numbers. Based on the study of minimal systems of generators, we choose an appropriate basis and give a complete classification of two step nilpotent Lie algebras of dimension 8.


two-step nilpotent Lie algebra base minimal system of generators related sets H-minimal system of generators 

MSC 2010

17B05 17B30 17B40 


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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2013

Authors and Affiliations

  1. 1.School of Mathematical Sciences and LPMCNankai UniversityTianjinP.R.China

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