Journal of Lie Theory 19 (2009), No. 2, 251--265
Copyright Heldermann Verlag 2009
Complex Structures on Quasi-Filiform Lie Algebras
Lucia García Vergnolle
Lab. de Mathématiques, Université de Haute Alsace, Faculté des Sciences et Techniques, 4 Rue des Frères Lumière, 68093 Mulhouse, France
lucigarcia@mat.ucm.es
Elizabeth Remm
Lab. de Mathématiques, Université de Haute Alsace, Faculté des Sciences et Techniques, 4 Rue des Frères Lumière, 68093 Mulhouse, France
The aim of this article is to classify quasi-filiform nilpotent Lie algebras g, that is with nilindex dim g-2, admitting a complex structure. Note that the non-existence of complex structures over nilpotent Lie algebras of maximal class, also called filiform, has already been proved by M. Goze and E. Remm [Non existence of complex structures on filiform Lie algebras, Comm. Algebra 30 (2002) 3777--3788].
Keywords: Complex structures, generalized complex structures, quasi-filiform Lie algebras.
MSC: 17B60, 53C56, 17B60
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