Cohomology and the controlling algebra of crossed homomorphisms on 3-Lie algebras

IF 0.5 3区 数学 Q3 MATHEMATICS
Shuai Hou, Meiyan Hu, Lina Song, Yanqiu Zhou
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引用次数: 0

Abstract

In this paper, first we give the notion of a crossed homomorphism on a 3-Lie algebra with respect to an action on another 3-Lie algebra, and characterize it using a homomorphism from a 3-Lie algebra to the semidirect product 3-Lie algebra. We also establish the relationship between crossed homomorphisms and relative Rota–Baxter operators of weight 1 on 3-Lie algebras. Next we construct a cohomology theory for a crossed homomorphism on 3-Lie algebras and classify infinitesimal deformations of crossed homomorphisms using the second cohomology group. Finally, using the higher derived brackets, we construct an L-algebra whose Maurer–Cartan elements are crossed homomorphisms. Consequently, we obtain the twisted L-algebra that controls deformations of a given crossed homomorphism on 3-Lie algebras.

同调与 3-李代数上交叉同态的控制代数
在本文中,我们首先给出了3-Lie代数上相对于另一个3-Lie代数上的作用的交叉同态的概念,并用从3-Lie代数到半直接积3-Lie代数的同态来描述它的特征。我们还建立了交叉同态与 3-Lie 代数上权重为 1 的相对 Rota-Baxter 算子之间的关系。接下来,我们构建了 3-Lie 代数上交叉同态的同调理论,并利用第二同调群对交叉同态的无限小变形进行了分类。最后,我们利用高阶导出括号,构造了一个 L∞-algebra ,其毛勒-卡尔坦元素是交叉同态。因此,我们得到了控制给定交叉同态在 3-Lie 代数上变形的扭曲 L∞-algebra 。
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来源期刊
CiteScore
1.50
自引率
12.50%
发文量
226
审稿时长
4-8 weeks
期刊介绍: The Journal of Algebra and Its Applications will publish papers both on theoretical and on applied aspects of Algebra. There is special interest in papers that point out innovative links between areas of Algebra and fields of application. As the field of Algebra continues to experience tremendous growth and diversification, we intend to provide the mathematical community with a central source for information on both the theoretical and the applied aspects of the discipline. While the journal will be primarily devoted to the publication of original research, extraordinary expository articles that encourage communication between algebraists and experts on areas of application as well as those presenting the state of the art on a given algebraic sub-discipline will be considered.
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