Letters to Alan Weinstein about Courant algebroids

TL;DR

This paper compiles letters from 1998-2000 discussing foundational results on Courant algebroids, including their classification, reduction, and connections to symplectic dg manifolds and Poisson-Lie T-duality.

Contribution

It provides a collection of fundamental results on Courant algebroids, including classification, reduction, and their relation to other geometric structures, advancing understanding of their properties.

Findings

Classification of exact and transitive Courant algebroids

Description of Courant algebroids via symplectic dg manifolds

Relation of Courant algebroids to Poisson-Lie T-duality

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.