What question did this study set out to answer?

The central aim is to classify quasi-filiform nilpotent Lie algebras that can support a complex structure.

March 29, 2026Open Access

Complex Structures on Quasi-Filiform Lie Algebras

Key Points

The central aim is to classify quasi-filiform nilpotent Lie algebras that can support a complex structure.
Classification of quasi-filiform nilpotent Lie algebras with nilindex dim g - 2.
Analysis of existing literature regarding complex structures in maximal class nilpotent Lie algebras.
Identification of conditions under which quasi-filiform nilpotent Lie algebras admit complex structures.
Confirmation that complex structures do not exist over nilpotent Lie algebras of maximal class (filiform).

Abstract

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 in 7.

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