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arXiv · 2505.01276

Manin triples on multiplicative Courant algebroids

Ana Carolina Mançur
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Abstract

We extend the characterization of Lie bialgebroids via Manin triples to the context of double structures over Lie groupoids. We consider Lie bialgebroid groupoids, given by LA-groupoids in duality, and establish their correspondence with multiplicative Manin triples, i.e., CA-groupoids equipped with a pair of complementary multiplicative Dirac structures. As an application, we give a new viewpoint to the co-quadratic Lie algebroids of Lang, Qiao, and Yin (2021) and the Manin triple description of Lie bialgebroid crossed modules.

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Ana Carolina Mançur. 2025-05-02. Manin triples on multiplicative Courant algebroids. https://doi.org/10.1016/j.difgeo.2025.102273

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