Won-Hak Ri , Ju-Song Jong , Un-Gyong Jong , Kwang-Hyon Jong
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引用次数: 0
Abstract
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.
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.
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