Proves a J-adapted Levi-Malcev decomposition for many 2-step solvable Lie algebras, confirming the Fino-Vezzoni conjecture for unimodular cases and characterizing SKT metrics on completely solvable ones.
Letters to Alan Weinstein about Courant algebroids
5 Pith papers cite this work. Polarity classification is still indexing.
5
Pith papers citing it
abstract
These letters, written in 1998-2000, contain various basic results about Courant algebroids (CAs), such as classification of exact and transitive CAs, reduction of CAs, description in terms of symplectic dg manifolds, a canonical generating Dirac operator, and a relation with Poisson-Lie T-duality.
years
2026 5representative citing papers
Courant algebroid relations define spinor and Dirac structure relations, with T-duality inducing spinor relations that generalize twisted cohomology isomorphisms and are compatible with Type II supergravity equations.
An explicit holomorphic theory is constructed for flux backgrounds in 10D N=1 supergravity, conjecturally realizing the supergravity twist and generalizing minimal type I BCOV theory via Courant algebroids.
The generalised Lie derivative of (s)pinor fields on Courant algebroids is constructed via a natural connection on the space of generalised metrics, yielding the formula L_u ψ = D_u ψ + (1/2)(D_u a^b)γ_{ab}ψ.
Establishes a correspondence between 2-shifted Lagrangian morphisms and Dirac structures, identifying multiplicative D-valued moment maps for integrating quasi-Poisson manifolds and constructing quasi-symplectic groupoids via fibred products.
citing papers explorer
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A Levi-type decomposition on two-step solvable Lie algebras with a complex structure
Proves a J-adapted Levi-Malcev decomposition for many 2-step solvable Lie algebras, confirming the Fino-Vezzoni conjecture for unimodular cases and characterizing SKT metrics on completely solvable ones.
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Generalised Complex and Spinor Relations
Courant algebroid relations define spinor and Dirac structure relations, with T-duality inducing spinor relations that generalize twisted cohomology isomorphisms and are compatible with Type II supergravity equations.
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Kodaira-Spencer theory for flux backgrounds
An explicit holomorphic theory is constructed for flux backgrounds in 10D N=1 supergravity, conjecturally realizing the supergravity twist and generalizing minimal type I BCOV theory via Courant algebroids.
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On the generalised Lie derivative of (s)pinor fields
The generalised Lie derivative of (s)pinor fields on Courant algebroids is constructed via a natural connection on the space of generalised metrics, yielding the formula L_u ψ = D_u ψ + (1/2)(D_u a^b)γ_{ab}ψ.
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Shifted lagrangian structures in Poisson geometry
Establishes a correspondence between 2-shifted Lagrangian morphisms and Dirac structures, identifying multiplicative D-valued moment maps for integrating quasi-Poisson manifolds and constructing quasi-symplectic groupoids via fibred products.