Rota-Baxter groups with weight zero and integration on topological groups
Xing Gao, Li Guo, Zongjian Han

TL;DR
This paper extends the concept of Rota-Baxter operators on groups to weight zero by using a novel perturbation approach, linking it to integrals on topological groups and a group version of the Fundamental Theorem of Calculus.
Contribution
It introduces a new definition of Rota-Baxter operators with weight zero on groups via a perturbation method, and explores their applications in topological groups and calculus.
Findings
Defined Rota-Baxter operators with weight zero on groups.
Connected the operators to integrals on topological groups.
Developed a group formulation of the Fundamental Theorem of Calculus.
Abstract
Rota-Baxter groups with weights have attracted quite much attention since their recent introduction, thanks to their connections with Rota-Baxter Lie algebras, factorizations of Lie groups, post- and pre-Lie algebras, braces and set-theoretic solutions of the Yang-Baxter equation. Despite their expected importance from integrals on groups to pre-groups and Yang-Baxter equations, Rota-Baxter groups with weight zero and other weights has been a challenge to define and their search has been the focus of several attempts. By composing an operator with a section map as a perturbation device, we first generalize the notion of a Rota-Baxter operator on a group from the existing case of weight to the case where the weight is given by a pair of maps and then a sequence limit of such pairs. From there, two candidates of Rota-Baxter operators with weight zero are given. One of…
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Taxonomy
TopicsAdvanced Topics in Algebra · Rings, Modules, and Algebras · Advanced Topology and Set Theory
