高阶 Omni-李代数胚 E-对偶
E-Value Dual of Higher Omni LieAlgebroids
DOI: 10.12677/PM.2023.132028, PDF, HTML,   
作者: 郑献聪：南昌航空大学数学与信息科学学院，江西 南昌
关键词: 高阶Omni-李代数胚； E-对偶； 高阶Omni李双代数Double；Higher Omni Lie Algebroids； E-Value Dual； Higher Omni Lie Bialgebroid Double
摘要: 该文研究了高阶 omni-李代数胚 E-对偶结构。首先，根据 E-值对偶丛的定义，在直和丛DnE⊕ℑE上定义了Dn-1E-值配对和高阶 Dorfman 括号，其中DnE和ℑE 分别为向量 E 的n-阶微分算子从和jet从。得到了高阶 omni-李代数 E-对偶结构。其次，通过莱布尼茨代数胚的匹配对，构造了与高阶 omni-李双代数胚相关的匹配对，并且得到了与平凡线丛 M× ℝ 相关的高阶omni-李双代数胚 double。
Abstract: In this paper, we study a E-value dual of higher omni Lie algebroids. First, we define Dn-1E-value pairing and higher Dorfman bracket on the direct sum bundle DnE⊕ℑE, where DnE and ℑE are, respectively, the n-th differential operator bundle and the jet bundle of a vector bundle E, construct a E-value dual of higher omni Lie algebroids.Secondly, through the matched pair of Leibniz algebras, construct a matched pair associated to higher omni Lie bialgebroid, and study higher omni Lie bialgebroid double associated to a trivial line bundle.
文章引用：郑献聪. 高阶 Omni-李代数胚 E-对偶[J]. 理论数学, 2023, 13(2): 234-243. https://doi.org/10.12677/PM.2023.132028

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