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Classification of Rota-Baxter operators on semigroup algebras of order two and three

In this paper, we determine all the Rota-Baxter operators of weight zero on semigroup algebras of order two and three with the help of computer algebra. We determine the matrices for these Rota-Baxter operators by directly solving the defining equations of the operators. We also produce a Mathematic...

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Detalles Bibliográficos
Autores principales: Zheng, Shanghua, Guo, Li, Rosenkranz, Markus
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Taylor & Francis 2019
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7083595/
https://www.ncbi.nlm.nih.gov/pubmed/32256224
http://dx.doi.org/10.1080/00927872.2018.1552278
Descripción
Sumario:In this paper, we determine all the Rota-Baxter operators of weight zero on semigroup algebras of order two and three with the help of computer algebra. We determine the matrices for these Rota-Baxter operators by directly solving the defining equations of the operators. We also produce a Mathematica procedure to predict and verify these solutions.