Lie 双桥体的多迪拉克结构

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2024-09-06 DOI:10.1016/j.difgeo.2024.102178

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引用次数: 0

摘要

在本文中，我们介绍了 Lie 双曲面的多狄拉克结构，它概括了流形上的多狄拉克结构和 Lie 双曲面上的狄拉克结构。接下来，我们还介绍了 Lie 布尔基的高阶 Courant 布尔基和 Lie 布尔基的高阶 Dorfman 布尔基，并研究了它们之间的关系。此外，我们还证明了特殊列双曲面的多狄拉克结构与列代数的高阶狄拉克结构之间存在一一对应关系。最后，我们利用列双曲面的多狄拉克结构构造了格尔斯滕哈伯代数。

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Multi-Dirac structures for Lie bialgebroids

In this paper, we introduce multi-Dirac structures for Lie bialgebroids, which generalize the multi-Dirac structures on manifolds and Dirac structures on Lie bialgebroids. Next, we also introduce higher-order Courant algebroids for Lie algebroids and higher-order Dorfman algebroids for Lie algebroids and study the relationship between them. Furthermore, we show that there is a one-to-one correspondence between the multi-Dirac structures for special Lie bialgebroids and the higher Dirac structures for Lie algebroids. Finally, we construct the Gerstenhaber algebra by using the multi-Dirac structure for Lie bialgebroids.

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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.