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Geometric structures on complex manifolds
October 4, 2011 11:40, Moscow
 


Some restrictions on existence of abelian complex structures

Isabel Dotti

University of Cordoba, Argentina
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Isabel Dotti


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Abstract: We describe the structure of Lie groups admitting left invariant abelian complex structures in terms of commutative associative algebras. More precisely, we consider a distinguished class of Lie algebras admitting abelian complex structures given by abelian double products. The structure of these Lie algebras can be described in terms of a pair of commutative associative algebras satisfying a compatibility condition. We will show that when $g$ is a Lie algebra with an abelian complex structure $J$, and $g$ decomposes as $g=u+Ju$, with $u$ an abelian subalgebra, then $g$ is an abelian double product.
Joint work with A. Andrada and M. L. Barberis.

Language: English

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