Operated groups, differential groups and Rota-Baxter groups with an emphasis on the free objects
Group Theory
2022-09-13 v1 Quantum Algebra
Rings and Algebras
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.
Cite
@article{arxiv.2209.04922,
title = {Operated groups, differential groups and Rota-Baxter groups with an emphasis on the free objects},
author = {Xing Gao and Li Guo and Yanjun Liu and Zhi-Cheng Zhu},
journal= {arXiv preprint arXiv:2209.04922},
year = {2022}
}
Comments
21 pages