{"title":"The Rota-Baxter algebra structures on split semi-quaternion algebra","authors":"Chen Quanguo, Deng Yong","doi":"arxiv-2409.07699","DOIUrl":null,"url":null,"abstract":"In this paper, we shall describe all the Rota-Baxter operators with any\nweight on split semi-quaternion algebra. Firstly, we give the matrix\ncharacterization of the Rota-Baxter operator on split semi-quaternion algebra.\nThen we give the corresponding matrix representations of all the Rota-Baxter\noperators with any weight on split semi-quaternion algebra. Finally, we shall\nprove that the Ma et al. results about the Rota-Baxter operators on Sweedler\nalgebra are just special cases of our results.","PeriodicalId":501136,"journal":{"name":"arXiv - MATH - Rings and Algebras","volume":"50 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Rings and Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.07699","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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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