Weak mirror symmetry of Lie algebras

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dc.creatorCleyton, R.
dc.creatorLauret, J.
dc.creatorPoon, Y. S.
dc.date2008-04-30
dc.date.accessioned2026-07-07T09:36:02Z
dc.date.available2026-07-07T09:36:02Z
dc.descriptionThe 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.
dc.description36 pages, 3 tables
dc.identifierhttps://arxiv.org/abs/0804.4787
dc.identifierhttp://arxiv.org/abs/0804.4787
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160035
dc.subjectAlgebraic Geometry
dc.subjectMathematical Physics
dc.subjectDifferential Geometry
dc.subject17B81 (Primary); 32G81, 16E45, 53D05 (Secondary)
dc.titleWeak mirror symmetry of Lie algebras
dc.typetext

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