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

Autor: Gao, Xing, Guo, Li, Liu, Yanjun, Zhu, Zhi-Cheng
Předmět:
Zdroj: Communications in Algebra; 2023, Vol. 51 Issue 11, p4481-4500, 20p
Abstrakt: 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. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index