带括号的韦尔斯型精确序列和代数代数交叉扩展

IF 1 3区数学 Q1 MATHEMATICS

Forum Mathematicum Pub Date : 2024-01-05 DOI:10.1515/forum-2023-0355

José Manuel Casas, Emzar Khmaladze, Manuel Ladra

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引用次数: 0

摘要

我们研究了与带括号代数的无边扩展相关的一对导数的可扩展性问题，并推导出韦尔斯类型的精确序列。我们为带括号的代数引入了交叉模块，并证明了它们与带括号代数范畴中的内部范畴的等价性。我们将交叉扩展的等价类集合解释为第二同调。最后，我们在带括号的代数共生中构建了一个八项精确序列。

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Wells-type exact sequence and crossed extensions of algebras with bracket

We study the extensibility problem of a pair of derivations associated with an abelian extension of algebras with bracket, and derive an exact sequence of the Wells type. We introduce crossed modules for algebras with bracket and prove their equivalence with internal categories in the category of algebras with bracket. We interpret the set of equivalence classes of crossed extensions as the second cohomology. Finally, we construct an eight-term exact sequence in the cohomology of algebras with bracket.

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来源期刊

Forum Mathematicum 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Forum Mathematicum is a general mathematics journal, which is devoted to the publication of research articles in all fields of pure and applied mathematics, including mathematical physics. Forum Mathematicum belongs to the top 50 journals in pure and applied mathematics, as measured by citation impact.