2006/10/26 by Adrián Andrada, Adrian Andrada, Andrada, Adrian
Mathematics · Physics and Astronomy · #17B60 #53C15 #53C30 #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #math.DG #msc:17B60 #msc:53C15 #msc:53C30
paper · pdf · doi:10.48550/arxiv.math/0610768
24 pages, to appear in Forum Math
arxiv created 2006/10/26 · openalex publication_date 2006/10/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study complex product structures on nilpotent Lie algebras, establishing some of their main properties, and then we restrict ourselves to 6 dimensions, obtaining the classification of 6-dimensional nilpotent Lie algebras admitting such structures. We prove that any complex structure which forms part of a complex product structure on a 6-dimensional nilpotent Lie algebra must be nilpotent in the sense of Cordero-Fernández-Gray-Ugarte. A study is made of the torsion-free connection associated to the complex product structure and we consider also the associated hypercomplex structures on the 12-dimensional nilpotent Lie algebras obtained by complexification.