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Abelian complex structures on solvable Lie algebras

M. L. Barberis·I. Dotti
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Abstract

We obtain a characterization of the real Lie algebras admitting abelian complex structures in terms of certain affine Lie algebras $\frak a \frak f \frak f (A)$, where $A$ is a commutative algebra. These affine Lie algebras are natural generalizations of $\frak a \frak f \frak f (\Bbb C)$ 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.

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M. L. Barberis, I. Dotti. 2002-02-21. Abelian complex structures on solvable Lie algebras. https://arxiv.org/abs/math/0202220

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