毕艳会, 杨一婷. 扩张的镜像Courant代数胚[J]. 南昌航空大学学报(自然科学版), 2020, 34(1): 21-25, 42. DOI: 10.3969/j.issn.1001-4926.2020.01.004
引用本文: 毕艳会, 杨一婷. 扩张的镜像Courant代数胚[J]. 南昌航空大学学报(自然科学版), 2020, 34(1): 21-25, 42. DOI: 10.3969/j.issn.1001-4926.2020.01.004
Yan-hui BI, Yi-ting YANG. Extended Mirror Courant Algebroids[J]. Journal of nanchang hangkong university(Natural science edition), 2020, 34(1): 21-25, 42. DOI: 10.3969/j.issn.1001-4926.2020.01.004
Citation: Yan-hui BI, Yi-ting YANG. Extended Mirror Courant Algebroids[J]. Journal of nanchang hangkong university(Natural science edition), 2020, 34(1): 21-25, 42. DOI: 10.3969/j.issn.1001-4926.2020.01.004

扩张的镜像Courant代数胚

Extended Mirror Courant Algebroids

  • 摘要: 在向量丛\calE ^1\left( M \right)上引入了扩张的镜像Courant代数胚。利用扩张的镜像Courant括号是通过向量丛自同构将\mathbbR变换为\mathbbR的对应于向量丛\calE ^1\left( M \right)上标准扩张的Courant括号的括号这个理论知识,研究了Courant代数胚镜像扩张下的代数几何结构,得出扩张的镜像Courant代数胚\cal Q_\Omega 为扩张的镜像Courant代数胚\cal Q_\Omega \Omega-扭转且扩张的镜像Courant代数胚的态射是它们各自扭转的态射的结论,也为研究Dirac丛提供了一种新的思路。

     

    Abstract: In this paper introduce extended mirror Courant algebroids and their mirror Dirac structures on the vector bundle \calE ^1\left( M \right). The extended mirror Courant bracket is the bracket corresponding to the standard extended Courant bracket on the vector bundle \calE ^1\left( M \right) via the vector bundle automorphism exchanging \mathbbR to \mathbbR. This paper is to study the algebraic geometry structures under the extend mirror Courant algebroids. We have found that the morphisms of the extended mirror Courant algebroids are the twisted and extennded mirror Courant algebroids, which are their respective twisted morphisms. Also provides a new idea for the study of Dirac bundle.

     

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