Complex structures on quasi-filiform nilpotent Lie algebras

TL;DR

This paper classifies real quasi-filiform nilpotent Lie algebras that admit complex structures, extending previous work on filiform cases to a broader class of nilpotent Lie algebras.

Contribution

It provides a complete classification of quasi-filiform nilpotent Lie algebras with complex structures, a case not previously fully explored.

Findings

Classification of quasi-filiform nilpotent Lie algebras with complex structures

Extension of known results from filiform to quasi-filiform cases

Identification of specific algebraic structures admitting complex structures

Abstract

We present the classification of real nilpotent quasi-filiform Lie algebras endowed with a complex structure. A nilpotent Lie algebra g is called quasi-filiform is the nilindex is equal to dim(n)-2. We recall that the filiform case (nilindex =dim(g)-1) has already been studied.