结合代数的Rota-Baxter模块匹配与𝒪-operators匹配

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Algebra and Its Applications Pub Date : 2023-11-03 DOI:10.1142/s021949882550094x

Huihui Zheng, Linlin Liu

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引用次数: 0

摘要

本文首先引入了匹配Rota-Baxter模块的概念，推广了匹配Rota-Baxter代数和Rota-Baxter模块的概念，并给出了其特征和构造。其次，给出了匹配Rota-Baxter模块与其他模块结构之间的关系。最后，引入了配对[公式:见文]算子的概念，推广了配对Rota-Baxter代数的概念，并利用配对[公式:见文]算子给出了共轭杨- baxter方程的偏振解。此外，我们引入了相容匹配[公式:见文]-关联代数算子、相容匹配尼金辉算子和相容匹配树形代数的定义，并考虑了它们之间的联系。

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Matching Rota-Baxter modules and Matching 𝒪-operators of associative algebras

In this paper, firstly, we introduce the notion of matching Rota–Baxter modules, which generalizes the notions of matching Rota–Baxter algebras and Rota–Baxter modules, and give its characteristic and construction. Secondly, we give the relation between matching Rota–Baxter modules and other modules structure. Finally, we introduce the notion of matching [Formula: see text]-operators of associative algebras which also generalizes the notion of matching Rota–Baxter algebras and give the solution of polarized associative Yang–Baxter equation by using the matching [Formula: see text]-operators of associative algebras. In addition, we introduce the definitions of the compatible matching [Formula: see text]-operators of associative algebras, matching Nijenhui operators, and compatible matching dendriform algebras, and consider their connection.

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来源期刊

Journal of Algebra and Its Applications 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

226

审稿时长

4-8 weeks

期刊介绍： The Journal of Algebra and Its Applications will publish papers both on theoretical and on applied aspects of Algebra. There is special interest in papers that point out innovative links between areas of Algebra and fields of application. As the field of Algebra continues to experience tremendous growth and diversification, we intend to provide the mathematical community with a central source for information on both the theoretical and the applied aspects of the discipline. While the journal will be primarily devoted to the publication of original research, extraordinary expository articles that encourage communication between algebraists and experts on areas of application as well as those presenting the state of the art on a given algebraic sub-discipline will be considered.