2008/04/30 by Richard Cleyton, Jorge Lauret, Cleyton, R. +3 · 1 citation
Mathematics · Physics and Astronomy · #16E45 #17B81 (Primary) #32G81 #53D05 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.0804.4787
openalex publication_date 2008/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.