Relative Rota-Baxter operators of weight 0 on groups, pre-groups, braces, the Yang-Baxter equation and $T$-structures

Abstract

In this paper, we study relative Rota-Baxter operators of weight $0$ on groups and give various examples. In particular, we propose different approaches to study Rota-Baxter operators of weight $0$ on groups and Lie groups. We establish various explicit relations among relative Rota-Baxter operators of weight $0$ on groups, pre-groups, braces, set-theoretic solutions of the Yang-Baxter equation and $T$-structures.

arXiv comment21 pages

References in corpus (10)

• Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and the main theorem
• Skew braces and the Yang-Baxter equation
• What a classical r-matrix really is
• Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras
• Integration and geometrization of Rota-Baxter Lie algebras
• Post-groups, (Lie-)Butcher groups and the Yang-Baxter equation
• Rota-Baxter operators on cocommutative Hopf algebras
• Skew braces of size $pq$
• Skew braces from Rota--Baxter operators: a cohomological characterisation and some examples
• Formality and finiteness in rational homotopy theory