On Lie Bialgebroid Crossed Modules

INTERNATIONAL JOURNAL OF MATHEMATICS（2021）

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摘要

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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关键词

Lie algebroid crossed modules, matched pair of Lie algebroids, Lie bialgebroids, Manin triples

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