论文标题
非亚伯嵌入张量
Nonabelian embedding tensors
论文作者
论文摘要
在本文中，首先，我们介绍了非亚伯嵌入张量的概念，这是嵌入张量的非亚伯概括。然后，我们介绍了leibniz-lie代数的概念，该代数是非亚伯嵌入张量的基础代数结构，也可以看作是莱布尼兹代数的非阿布尔概括。接下来，我们使用派生的支架，构建一个差分级的lie代数，其毛勒 - 卡丹元素正是nonabelian嵌入张量。因此，我们获得了控制非亚伯嵌入张量的变形的差分级谎言代数。最后，我们定义了非亚伯嵌入张量的共同体，并使用第二个同胞组来表征线性变形。
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.
