莱布尼兹代数交叉同态的同调与变形理论

Pub Date : 2024-02-14 DOI:10.1142/s0219498825501956

Yizheng Li, Dingguo Wang

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引用次数: 0

摘要

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。

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Cohomology and deformation theory of crossed homomorphisms of Leibniz algebras

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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