Courant Algebroids and Strongly Homotopy Lie Algebras

TL;DR

This paper explores the relationship between Courant algebroids and strongly homotopy Lie algebras, showing that Courant algebroids can be viewed as examples of these higher algebraic structures, with implications for Poisson geometry.

Contribution

It demonstrates that Courant algebroids can be interpreted as strongly homotopy Lie algebras, extending their understanding within higher algebraic frameworks.

Findings

Courant algebroids include doubles of Lie bialgebras and tangent-cotangent bundles.

They can be constructed as doubles of Lie bialgebroids, relevant to Poisson groupoids.

Courant algebroids are shown to be strongly homotopy Lie algebras.

Abstract

Courant algebroids are structures which include as examples the doubles of Lie bialgebras and the direct sum of tangent and cotangent bundles with the bracket introduced by T. Courant for the study of Dirac structures. Within the category of Courant algebroids one can construct the doubles of Lie bialgebroids, the infinitesimal objects for Poisson groupoids. We show that Courant algebroids can be considered as strongly homotopy Lie algebras.