修正λ差分左对称代数和交叉模块的阿贝尔扩展

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-04 DOI:10.3390/axioms13060380

Fuyang Zhu, Taijie You, Wen Teng

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引用次数: 0

摘要

本文定义了修正λ差分左对称代数的同调理论。此外，我们还引入了修正λ差分左对称 2-代数的概念，即修正λ差分左对称代数的分类。作为同调的应用，我们用第二同调群对修正λ-差分左对称代数的线性变形和无边扩展进行了分类，并用第三同调群对骨骼修正λ-差分左对称 2-代数进行了分类。最后，我们证明了严格修正λ-差分左对称 2-代数等价于修正λ-差分左对称代数的交叉模块。

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Abelian Extensions of Modified λ-Differential Left-Symmetric Algebras and Crossed Modules

In this paper, we define a cohomology theory of a modified λ-differential left-symmetric algebra. Moreover, we introduce the notion of modified λ-differential left-symmetric 2-algebras, which is the categorization of a modified λ-differential left-symmetric algebra. As applications of cohomology, we classify linear deformations and abelian extensions of modified λ-differential left-symmetric algebras using the second cohomology group and classify skeletal modified λ-differential left-symmetric 2-algebra using the third cohomology group. Finally, we show that strict modified λ-differential left-symmetric 2-algebras are equivalent to crossed modules of modified λ-differential left-symmetric algebras.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.