Cohomology of Hom-Associative Algebras in Loday–Pirashvili Category with Applications

IF 0.7 4区数学 Q2 MATHEMATICS

Bulletin of The Iranian Mathematical Society Pub Date : 2024-08-14 DOI:10.1007/s41980-024-00905-9

Tao Zhang

引用次数: 0

Abstract

We introduce the concept of Hom-associative algebra structures in Loday–Pirashvili category. The cohomology theory of Hom-associative algebras in this category is studied. Some applications on deformation and abelian extension theory are given. We also introduce the notion of Nijenhuis operators to describe trivial deformations. It is proved that equivalent classes of abelian extensions are one-to-one correspondence to the elements of the second cohomology groups.

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Loday-Pirashvili 类别中 Hom-Associative 算法的同调及其应用

我们介绍了 Loday-Pirashvili 范畴中 Hom-associative 代数结构的概念。研究了该范畴中的同调代数理论。给出了变形和无性延伸理论的一些应用。我们还引入了尼延胡斯算子的概念来描述琐碎变形。研究证明，等价类的无性延伸与第二同调群的元素是一一对应的。

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

Bulletin of The Iranian Mathematical Society Mathematics-General Mathematics

CiteScore

1.40

自引率

0.00%

发文量

期刊介绍： The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.