广义n-omni-李代数胚  

Generalized n-omni-Lie Algebroids

作　　者：毕艳会[1] 郑献聪 BI Yan-hui;ZHENG Xian-cong(Center for Mathematical Sciences,College of Mathematics and Information Science,Nanchang Hangkong University,Nanchang 330063,China)

机构地区：[1]南昌航空大学,数学与信息科学学院,数学中心,南昌330063

出　　处：《南昌航空大学学报（自然科学版）》2023年第1期44-49,67,共7页Journal of Nanchang Hangkong University(Natural Sciences)

基　　金：国家自然科学基金(11961049,11601219)。

摘　　要：本文研究广义n-omni-李代数胚结构。首先,在直和丛D_(0)^(N)E⊕JE上定义D^(n-1)值配对和高阶Dorfman括号,构造广义n-omni-李代数胚,证明广义n-omni-李代数胚具有与n-omni-李代数胚类似的性质。其次,当E为平凡线丛时,构造截面Γ(ε^(n))上的高阶Dorfman括号,得到与平凡线丛_(M×R)相关的广义n-omni-李代数胚ε^(n)_(M×R)。最后,给出广义n-omni-李代数胚高阶Dirac结构,并证明图Gr(B_(△))为广义n-omni-李代数胚的高阶Dirac结构。In this paper,we report the structure of generalized n-omni-Lie algebroids.Firstly,the definitions of a D^(n-1)E-value pairing and a higher Dorfman bracket are given on the direct sum bundle D_(0)^(N)E⊕JE.The generalized n-omni-Lie algebroids are constructed and their properties are proved and similar to those of n-omni-Lie algebroids.Secondly,when E is a trivial line bundle,a higher Dorfman bracket is constructed on the sectionΓ(ε^(n))to obtain the generalized n-omni-Lie algebroidsε^(n)(M×R)associated to a trivial line bundle_(M×R)Finally,the higher Dirac structure of the generalized n-omni-Lie algebroid is presented,and the graph Gr(B_(△))is verified as the higher Dirac structure of generalized n-omni-Lie algebroids.

关 键 词：广义n-omn-李代数胚 平凡线丛_(M×R) DIRAC结构 Dorfman括号 

分 类 号：O152.5[理学—数学]