On Lie Bialgebroid Crossed Modules

Abstract

We study Lie bialgebroid crossed modules which are pairs of Lie algebroid crossed modules in duality that canonically give rise to Lie bialgebroids. A one-one correspondence between such Lie bialgebroid crossed modules and co-quadratic Manin triples $(K,P,Q)$ is established, where $K$ is a co-quadratic Lie algebroid and $(P,Q)$ is a pair of transverse Dirac structures in $K$.

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References in corpus (1)

• Obstruction classes of crossed modules of Lie algebroids and Lie groupoids linked to existence of principal bundles