关于津比尔代数和罗塔-巴克斯特算子的若干结果

Axioms Pub Date : 2024-05-10 DOI:10.3390/axioms13050314

Jizhong Gao, Junna Ni, Jianhua Yu

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引用次数: 0

摘要

罗塔-巴克斯特算子（Rota-Baxter operator，RBO）在数学的许多分支领域，尤其是数学物理中发挥着重要作用。文章首先研究了津比尔代数（ZA）及其子邻接代数上的 RBO。此外，还介绍了二维和三维 ZAs 上的所有 RBO。最后，在交换关联代数的 RBO 的低维度中也实现了 ZA。研究发现，并非所有的 ZA 都可以通过这种方式实现。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Some Results on Zinbiel Algebras and Rota–Baxter Operators

Rota–Baxter operators (RBOs) play a substantial role in many subfields of mathematics, especially in mathematical physics. In the article, RBOs on Zinbiel algebras (ZAs) and their sub-adjacent algebras are first investigated. Moreover, all the RBOs on two and three-dimensional ZAs are presented. Finally, ZAs are also realized in low dimensions of the RBOs of commutative associative algebras. It was found that not all ZAs can be attained in this way.

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