Quasi-triangular pre-Lie bialgebras, factorizable pre-Lie bialgebras and Rota-Baxter pre-Lie algebras

DOI10.1016/j.geomphys.2024.105146MaRDI QIDQ6204225

Jiefeng Liu, You Wang, Yun He Sheng, Cheng-Ming Bai

Publication date: 27 March 2024

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

zbMATH Keywords

factorizable pre-Lie Bialgebramatched pair of Rota-Baxter pre-Lie algebrasquadratic Rota-Baxter pre-Lie algebraquasi-triangular pre-Lie BialgebraRota-Baxter pre-Lie Bialgebra

Mathematics Subject Classification ID

Lie bialgebras; Lie coalgebras (17B62) Nonassociative algebras satisfying other identities (17A30) Yang-Baxter equations and Rota-Baxter operators (17B38)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Abelian para-Kähler structures on Lie algebras
• Generalized Lax pairs, the modified classical Yang-Baxter equation, and affine geometry of Lie groups
• An analytic problem whose solution follows from a simple algebraic identity
• What is a classical r-matrix?
• Four dimensional symplectic Lie algebras
• Quantization and dynamisation of trace-Poisson brackets
• Quantum R-matrices and factorization problems
• Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras
• Homogeneous Hessian manifolds
• Homogeneous symplectic manifolds and dipolarizations in Lie algebras
• Poisson structures on double Lie groups
• Simple finite-dimensional double algebras
• On Rota-Baxter operators of non-zero weight arisen from the solutions of the classical Yang-Baxter equation
• Algebraic structures of \(F\)-manifolds via pre-Lie algebras
• Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
• Double Lie algebras of a nonzero weight
• \(F\)-manifold algebras and deformation quantization via pre-Lie algebras
• Rota-Baxter operators and non-skew-symmetric solutions of the classical Yang-Baxter equation on quadratic Lie algebras
• On para-Kähler and hyper-para-Kähler Lie algebras
• Left-symmetric algebras, or pre-Lie algebras in geometry and physics
• Symplectic structures on quadratic Lie algebras
• Factorizable Lie bialgebras, quadratic Rota-Baxter Lie algebras and Rota-Baxter Lie bialgebras
• LEFT-SYMMETRIC BIALGEBRAS AND AN ANALOGUE OF THE CLASSICAL YANG–BAXTER EQUATION
• Rota-Baxter operators on pre-Lie algebras
• On the Nature of the Virasoro Algebra
• What a Classical r-Matrix Really Is
• Formality of Kapranov's Brackets in Kähler Geometry via Pre-Lie Deformation Theory
• Field Algebras
• Non-Abelian phase spaces
• An Introduction to Pre‐Lie Algebras
• A unified algebraic approach to the classical Yang–Baxter equation
• Pre-Lie deformation theory
• Symplectic Homogeneous Spaces

This page was built for publication: Quasi-triangular pre-Lie bialgebras, factorizable pre-Lie bialgebras and Rota-Baxter pre-Lie algebras