$T$-duality on nilmanifolds

Abstract

We study generalized complex structures and $T$-duality (in the sense of Bouwknegt, Evslin, Hannabuss and Mathai) on Lie algebras and construct the corresponding Cavalcanti and Gualtieri map. Such a construction is called "Infinitesimal $T$-duality". As an application we deal with the problem of finding symplectic structures on 2-step nilpotent Lie algebras. We also give a criteria for the intregability of the infinitesimal $T$-duality of Lie algebras to topological $T$-duality of the associated nilmanifolds.

V2: minor corrections and a reference added

References in corpus (5)

• T-duality for principal torus bundles
• Family Floer cohomology and mirror symmetry
• Nilradicals of parabolic subalgebras admitting symplectic structures
• Symplectic structures on 2-step nilpotent Lie algebras
• On generalized $G_2$-structures and $T$-duality

Cited by in corpus (3)

• On generalized $G_2$-structures and $T$-duality
• Towards a T-dual Emergent Gravity
• Heterotic solitons on four-manifolds