分裂半四元数代数上的罗塔-巴克斯特代数结构

arXiv - MATH - Rings and Algebras Pub Date : 2024-09-12 DOI:arxiv-2409.07699

Chen Quanguo, Deng Yong

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引用次数: 0

摘要

本文将描述所有在分裂半四元数代数上具有任意权重的罗塔-巴克斯特算子。首先，我们给出了分裂半四元数代数上 Rota-Baxter 算子的矩阵特征，然后给出了分裂半四元数代数上所有任意权 Rota-Baxter 算子的相应矩阵表示。最后，我们将证明 Ma 等人关于 Sweedleralgebra 上 Rota-Baxter 算子的结果只是我们结果的特例。

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The Rota-Baxter algebra structures on split semi-quaternion algebra

In this paper, we shall describe all the Rota-Baxter operators with any weight on split semi-quaternion algebra. Firstly, we give the matrix characterization of the Rota-Baxter operator on split semi-quaternion algebra. Then we give the corresponding matrix representations of all the Rota-Baxter operators with any weight on split semi-quaternion 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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arXiv - MATH - Rings and Algebras

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