Abelian complex structures on solvable Lie algebras

Abstract

We obtain a characterization of the real Lie algebras admitting abelian complex structures in terms of certain affine Lie algebras $\mathfrak{aff}(A)$, where $A$ is a commutative algebra. These affine Lie algebras are natural generalizations of $\mathfrak{aff}(\mathbb{C})$ and the corresponding Lie groups are complex affine manifolds. It turns out that all 4-dimensional Lie algebras carrying abelian complex structures are central extensions of such affine Lie algebras.

8 pages

References in corpus (1)

• Geometry of Hyper-Kähler Connections with Torsion

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