Nonabelian embedding tensors
Nonabelian embedding tensors
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DOI：
10.1007/s11005-023-01637-3
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发表时间：
2022-04
影响因子：
1.2
通讯作者：
Rong Tang;Y. Sheng
中科院分区：
文献类型：
--
作者：
Rong Tang;Y. Sheng
在本文中，我们首先引入了非交换嵌入张量的概念，它是嵌入张量的非交换推广。然后，我们引入了莱布尼兹-李代数的概念，这是一个nonabel嵌入张量的基本代数结构，也可以被看作是一个莱布尼兹代数的nonabel推广。然后利用导出的括号构造了一个微分分次李代数，其Maurer-Cartan元恰好是非交换嵌入张量。因此，我们得到的微分分次李代数的非交换嵌入张量的变形。最后，我们定义了非阿贝尔嵌入张量的上同调，并使用第二上同调群来表征线性变形。
In this paper, first we introduce the notion of a nonabelian embedding tensor, which is a nonabelian generalization of an embedding tensor. Then, we introduce the notion of a Leibniz–Lie algebra, which is the underlying algebraic structure of a nonabelian embedding tensor, and can also be viewed as a nonabelian generalization of a Leibniz algebra. Next using the derived bracket, we construct a differential graded Lie algebra, whose Maurer–Cartan elements are exactly nonabelian embedding tensors. Consequently, we obtain the differential graded Lie algebra that governs deformations of a nonabelian embedding tensor. Finally, we define the cohomology of a nonabelian embedding tensor and use the second cohomology group to characterize linear deformations.