Complex structures on nilpotent Lie algebras with one-dimensional center
Adela Latorre, Luis Ugarte, Raquel Villacampa
Abstract
We classify the nilpotent Lie algebras of real dimension eight and minimal center that admit a complex structure. Furthermore, for every such nilpotent Lie algebra g, we describe the space of complex structures on g up to isomorphism. As an application, the nilpotent Lie algebras having a non-trivial abelian J-invariant ideal are classified up to eight dimensions.
Topics & Concepts
MathematicsNilpotentPure mathematicsLie algebraCentral seriesCenter (category theory)Isomorphism (crystallography)Lie conformal algebraNilpotent groupAbelian groupAlgebra over a fieldCrystal structureChemistryCrystallographyAdvanced Topics in AlgebraGeometry and complex manifoldsAdvanced Algebra and Geometry