论文标题
Hom-Leibniz-rinehart代数的共同体学和交叉模块扩展
Cohomology and crossed modules extension of Hom-Leibniz-Rinehart algebras
论文作者
论文摘要
在本文中，我们介绍了Hom-Leibniz-Rinehart代数的交叉模块的概念。我们研究霍姆 - 莱布尼斯 - 里纳特代数的同时和扩展理论。事实证明，霍姆 - 莱布尼斯 - 里纳哈特代数的阿贝尔扩展与第二个共同体学组的元素之间存在一对一的对应关系。此外，我们证明，从$α$划线的模块扩展到Hom-Leibniz-Rinehart代数到Hom-Leibniz-rinehart代数的第三个同居组。
In this paper, we introduce the concept of crossed module for Hom-Leibniz-Rinehart algebras. We study the cohomology and extension theory of Hom-Leibniz-Rinehart algebras. It is proved that there is one-to-one correspondence between equivalence classes of abelian extensions of Hom-Leibniz-Rinehart algebras and the elements of second cohomology group. Furthermore, we prove that there is a natural map from $α$-crossed modules extension of Hom-Leibniz-Rinehart algebras to the third cohomology group of Hom-Leibniz-Rinehart algebras.
