Weak mirror symmetry of Lie algebras

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The existence of a flat torsion-free connection, or left symmetric algebra structure on a Lie algebra g gives rise to a canonically defined complex structure on g+g and a symplectic structure on g+g^*. We verify that the associated differential Gerstenhaber algebras controlling the deformation theories of the complex and symplectic form are isomorphic. This provides a class of examples of "weak mirror symmetry" as suggested by Merkulov. For nilpotent algebras in dimension 4 and 6 the isomorphism classes of the semi-direct products g+g and g+g^* are listed. A one-parameter family of inequivalent pseudo-Kähler structures is given.
36 pages, 3 tables

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Algebraic Geometry, Mathematical Physics, Differential Geometry, 17B81 (Primary); 32G81, 16E45, 53D05 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/160035

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0804.4787
 http://arxiv.org/abs/0804.4787

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arXiv