乘法Courant代数上的Manin三元组

IF 0.7 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2025-08-01 DOI:10.1016/j.difgeo.2025.102273

Ana Carolina Mançur

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引用次数: 0

摘要

我们通过Manin三元组将李双代数群的表征推广到李群上的双结构。我们考虑由对偶性的la -群拟给出的李双代数群拟，并建立了它们与乘法Manin三元组的对应关系，即ca -群拟具有一对互补的乘法Dirac结构。作为应用，我们给出了Lang、Qiao、Yin的共二次李代数体和李双代数体交叉模的Manin三重描述的新观点。

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Manin triples on multiplicative Courant algebroids

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 [13] and the Manin triple description of Lie bialgebroid crossed modules.

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.