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, 下载: 229  浏览: 336 
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

参考文献

[1] Chen, Z. and Liu, Z. (2010) Omni-Lie Alegebroids. Journal of Geometry and Physics, 60, 799-808.
https://doi.org/10.1016/j.geomphys.2010.01.007
[2] Bi, Y., Vitagliano, L. and Zhang, T. (2018) Higher Omni-Lie Algebroids. arXiv preprint arXiv:1812.09496
[3] Lang, H. and Sheng, Y. (2020) Linearization of the Higher Analogue of Courant Algebroids. Journal of Geometric Mechanics, 12, 585-606.
https://doi.org/10.3934/jgm.2020025
[4] Ibanez, R., Leon, M. and Marrero, J. (1997) Dynamics of Generalized Poisson and Nambu- Poisson Brackets. Journal of Mathematical Physics, 38, 2332-2344.
https://doi.org/10.1063/1.531960
[5] Saunders, D.J., Saunders, D. and Saunders, D.J. (1989) The Geometry of Jet Bundles. Cambridge University Press, Cambridge.
https://doi.org/10.1017/CBO9780511526411
[6] Chen, Z., Liu, Z. and Sheng, Y. (2010) E-Courant Algebroids. International Mathematics Research Notices, 2010, 4334-4376.
https://doi.org/10.1093/imrn/rnq053
[7] Crainic, M. and Moerdijk, I. (2008) Deformations of Lie Brackets: Cohomological Aspects.Journal of the European Mathematical Society, 10, 1037-1059.
https://doi.org/10.4171/JEMS/139
[8] Sheng, Y. (2012) On Deformations of Lie Algebroids. Results in Mathematics, 62, 103-120.
https://doi.org/10.1007/s00025-011-0133-x
[9] 毕艳会, 范宏涛, 陈丹露. 非交换omni-李代数胚[J]. 数学进展, 2022, 51(5): 879-890.
[10] Liu, Z.J., Weinstein, A. and Xu, P. (1997) Manin Triples for Lie Bialgebroids. Journal of Differential Geometry, 45, 547-574.
https://doi.org/10.4310/jdg/1214459842
[11] Ibaez, R., Lopez, B., Marrero, J.C., et al. (2001) Matched Pairs of Leibniz Algebroids, NambuJacobi Structures and Modular Class. Comptes Rendus de l'Academie des Sciences-Series I-Mathematics, 333, 861-866.
https://doi.org/10.1016/S0764-4442(01)02150-4
[12] Bi, Y. and Fan, H. (2021) Higher Nonabelian Omni-Lie Algebroids. Journal of Geometry and Physics, 167, Article ID: 104277.
https://doi.org/10.1016/j.geomphys.2021.104277

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