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The classification of two step nilpotent complex Lie algebras of dimension 8. (English) Zbl 1291.17013

The classification of complex nilpotent Lie algebras of small dimension has a long history, yet only for dimension less than or equal to seven has it been completed. Further advancements have been made by putting conditions on the algebra and that is the strategy in this paper. The authors classify complex Lie algebras that are two step nilpotent. Thus for these algebras, the derived algebra is contained in the center. The problem is reduced to the cases when the center has dimension 2, 3 or 4. R. Bin and L. S. Zhu solved the problem when the center is 2-dimensional [Commun. Algebra 39, No. 6, 2068–2081 (2011; Zbl 1290.17004)]. In this paper the authors complete the other two cases.

MSC:

17B30 Solvable, nilpotent (super)algebras
17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras
17B05 Structure theory for Lie algebras and superalgebras

Citations:

Zbl 1290.17004
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References:

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