Classification of abelian complex structures on 6-dimensional Lie algebras

A. ANDRADA, M.L. BARBERIS, I. DOTTI

Marburg, Alemania

Workshop; Workshop on Dirac Operators and Special Geometries; 2009

Philipps Universität, Marburg

Abelian complex structures on solvmanifolds have interesting applications in hyper-Kähler withtorsion geometry and a nilmanifold with such a structure has the advantage that its Dolbeault cohomology can be computed algebraically. In this talk, after giving the basic background, we will sketch the classification of the 6-dimensional simply connected Lie groups which can be endowed with a left-invariant abelian complex structure. We will also exhibit the parameterization, on each of the corresponding Lie algebras, of the space of such structures up to equivalence.