分裂半四元数代数上的Rota-Baxter代数结构

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-07-07 DOI:10.1002/mma.11218

Quanguo Chen, Yong Deng

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引用次数: 0

摘要

在本文中，我们将描述分裂半四元数代数上所有具有任意权值的Rota-Baxter算子。首先给出了分裂半四元数代数上Rota-Baxter算子的矩阵刻画。然后给出了在分裂半四元数代数上所有具有任意权值的Rota-Baxter算子的对应矩阵表示。最后，我们将证明关于Sweedler代数上Rota-Baxter算子的Ma等人的结果只是我们的结果的特殊情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

The Rota-Baxter Algebra Structures on Split Semiquaternion Algebra

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The Rota-Baxter Algebra Structures on Split Semiquaternion Algebra

In this paper, we shall describe all the Rota-Baxter operators with any weight on split semiquaternion algebra. Firstly, we give the matrix characterization of the Rota-Baxter operator on split semiquaternion algebra. Then we give the corresponding matrix representations of all the Rota-Baxter operators with any weight on split semiquaternion algebra. Finally, we shall prove that the Ma et al. results about the Rota-Baxter operators on Sweedler algebra are just special cases of our results.

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.