Cohomology and deformation theory of crossed homomorphisms of Leibniz algebras

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Algebra and Its Applications Pub Date : 2024-02-14 DOI:10.1142/s0219498825501956

Yizheng Li, Dingguo Wang

引用次数: 0

Abstract

In this paper, we construct a differential graded Lie algebra whose Maurer–Cartan elements are given by crossed homomorphisms on Leibniz algebras. This allows us to define cohomology for a crossed homomorphism. Finally, we study linear deformations, formal deformations and extendibility of finite order deformations of a crossed homomorphism in terms of the cohomology theory.

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莱布尼兹代数交叉同态的同调与变形理论

在本文中，我们构建了一个微分级数李代数，它的毛勒-卡尔坦元素是由莱布尼兹代数上的交叉同态给出的。这使我们能够定义交叉同态的同调。最后，我们用同调理论研究了交叉同态的线性变形、形式变形和有限阶变形的可扩展性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Algebra and Its Applications 数学-数学

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.