Operated groups, differential groups and Rota-Baxter groups with an emphasis on the free objects

Xing Gao; Li Guo; Yanjun Liu; Zhi-Cheng Zhu

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arXiv · 2209.04922

Operated groups, differential groups and Rota-Baxter groups with an emphasis on the free objects

Xing Gao·Li Guo·Yanjun Liu·Zhi-Cheng Zhu

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Abstract

Groups with various types of operators, in particular the recently introduced Rota-Baxter groups, have generated renowned interest with close connections to numerical integrals, Yang-Baxter equation, integrable systems and post-Hopf algebras. This paper gives the general notion of operated groups and provides explicit constructions of free operated groups, free differential groups and free Rota-Baxter groups.

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Xing Gao, Li Guo, Yanjun Liu, Zhi-Cheng Zhu. 2022-09-11. Operated groups, differential groups and Rota-Baxter groups with an emphasis on the free objects. https://arxiv.org/abs/2209.04922

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