Results 1 to 10 of about 85 (73)

Rota–Baxter operators on Clifford semigroups and the Yang–Baxter equation

Journal of Algebra, 2023
In this paper, we introduce the theory of Rota-Baxter operators on Clifford semigroups, useful tools for obtaining dual weak braces, i.e., triples $\left(S,+,\circ\right)$ where $\left(S,+\right)$ and $\left(S,\circ\right)$ are Clifford semigroups such that $a\circ\left(b+c\right) = a\circ b - a +a\circ c$ and $a\circ a^- = -a+a$, for all $a,b,c\in S$.
Francesco Catino, Paola Stefanelli, Marzia Mazzotta   +2 more
exaly   +5 more sources

Rota-Baxter operators on $\mathrm{sl(2,\mathbb {C})}$ sl (2,C) and solutions of the classical Yang-Baxter equation [PDF]

Journal of Mathematical Physics, 2014
We explicitly determine all Rota-Baxter operators (of weight zero) on $\mathrm{sl(2,\mathbb {C})}$ sl (2,C) under the Cartan-Weyl basis. For the skew-symmetric operators, we give the corresponding skew-symmetric solutions of the classical Yang-Baxter equation in $\mathrm{sl(2,\mathbb {C})}$ sl (2,C), confirming the related study by Semenov-Tian-Shansky.
Li Guo, Chengming Bai, Bai Chengming
exaly   +2 more sources

Yang-Baxter Equations and Relative Rota-Baxter Operators for Left-Alia Algebras Associated to Invariant Theory

Journal of Nonlinear Mathematical Physics
arXiv admin note: text overlap with arXiv:2403 ...
Guilai Liu
exaly   +3 more sources

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

Annali Di Matematica Pura Ed Applicata
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 ...
Rong Tang, Yunhe Sheng, Sheng Yunhe
exaly   +3 more sources

Zinbiel bialgebras, relative Rota-Baxter operators and the related Yang-Baxter equation

Journal of Algebra
In this paper, we first introduce the notion of a Zinbiel bialgebra and show that Zinbiel bialgebras, matched pairs of Zinbiel algebras and Manin triples of Zinbiel algebras are equivalent. Then we study the coboundary Zinbiel bialgebras, which leads to an analogue of the classical Yang-Baxter equation.
exaly   +3 more sources

Rota-Baxter operators on crossed modules of Lie groups and categorical solutions of the Yang-Baxter equation

Journal of Geometry and Physics
In this paper, we construct a categorical solution $(\huaC, R)$ of the Yang-Baxter equation, i.e. $\huaC$ is a small category and $R: \huaC\times\huaC\lon\huaC\times\huaC$ is an invertible functor satisfying $$ (R\times\Id_\huaC)(\Id_\huaC\times R)(R\times\Id_\huaC)=(\Id_\huaC\times R)(R\times\Id_\huaC)(\Id_\huaC\times R), $$ where $\huaC\times\huaC ...
exaly   +3 more sources

Leibniz bialgebras, relative Rota–Baxter operators, and the classical Leibniz Yang–Baxter equation [PDF]

Journal of Noncommutative Geometry, 2022
In this paper, first we introduce the notion of a Leibniz bialgebra and show that matched pairs of Leibniz algebras, Manin triples of Leibniz algebras, and Leibniz bialgebras are equivalent. Then we introduce the notion of a (relative) Rota–Baxter operator on a Leibniz algebra and construct the graded Lie algebra that characterizes
Rong Tang, Yunhe Sheng
openaire   +3 more sources

Post-Hopf algebras, relative Rota–Baxter operators and solutions to the Yang–Baxter equation

Journal of Noncommutative Geometry, 2023
In this paper, first, we introduce the notion of post-Hopf algebra, which gives rise to a post-Lie algebra on the space of primitive elements and the fact that there is naturally a post-Hopf algebra structure on the universal enveloping algebra of a post-Lie algebra. A novel property is that a cocommutative post-Hopf algebra gives rise to a generalized
Yunnan Li, Yunhe Sheng, Rong Tang
openaire   +3 more sources

-Rota–Baxter Operators, Infinitesimal Hom-bialgebras and the Associative (Bi)Hom-Yang–Baxter Equation [PDF]

Canadian Mathematical Bulletin, 2019
AbstractWe introduce the concept of a $\{\unicode[STIX]{x1D70E},\unicode[STIX]{x1D70F}\}$ -Rota–Baxter operator, as a twisted version of a Rota–Baxter operator of weight zero. We show how to obtain a certain $\{\unicode[STIX]{x1D70E},\unicode[STIX]{x1D70F}\}$ -Rota–Baxter operator from
Liu L., Makhlouf A., Menini C., Panaite F.   +3 more
openaire   +3 more sources

Rota-Baxter operators on $sl(2,C)$ and solutions of the classical Yang-Baxter equation

, 2013
17 ...
Pei, Jun, Bai, Chengming, Guo, Li
openaire   +2 more sources