Left-symmetric algebroids
Left-symmetric algebroids
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左对称代数体
DOI：
10.1002/mana.201300339
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发表时间：
2016
影响因子：
1
通讯作者：
Zhiqi Chen
中科院分区：
文献类型：
--
作者：
Jiefeng Liu;Yunhe Sheng;Chengming Bai;Zhiqi Chen
在本文中，我们引入了左对称代数胚的概念，它是左对称代数从向量空间到向量丛的推广。左乘法产生对应的次相邻李代数胚的表示。我们从李代数胚上的-算子构造左对称代数胚。我们用左对称代数胚来研究李代数胚的相空间。详细研究了左对称代数胚的表示。最后，我们研究了左对称代数胚的变形，它可以由变形上同调中的第二上同调类控制。
In this paper, we introduce the notion of a left‐symmetric algebroid, which is a generalization of a left‐symmetric algebra from a vector space to a vector bundle. The left multiplication gives rise to a representation of the corresponding sub‐adjacent Lie algebroid. We construct left‐symmetric algebroids from ‐operators on Lie algebroids. We study phase spaces of Lie algebroids in terms of left‐symmetric algebroids. Representations of left‐symmetric algebroids are studied in detail. At last, we study deformations of left‐symmetric algebroids, which could be controlled by the second cohomology class in the deformation cohomology.