Post-groups, (Lie-)Butcher groups and the Yang-Baxter equation

DOI10.1007/s00208-023-02592-zarXiv2306.11196MaRDI QIDQ6198272

Rong Tang, Yun He Sheng, Cheng-Ming Bai, Li Guo

Publication date: 21 February 2024

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2306.11196

zbMATH Keywords

Yang-Baxter equationpost-groups(Lie-)Butcher groups

Mathematics Subject Classification ID

Lie algebras of Lie groups (22E60) Numerical methods for ordinary differential equations (65L99) Hopf algebras and their applications (16T05) Yang-Baxter equations (16T25) Operads (general) (18M60) Yang-Baxter equations and Rota-Baxter operators (17B38)

Related Items

Operated groups, differential groups and Rota-Baxter groups with an emphasis on the free objects, Pure quadratization and solution of ordinary differential equations by probabilistic evolution theory with concurrent computation of coefficients using exact arithmetic

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Commutative post-Lie algebra structures on Lie algebras
• On post-Lie algebras, Lie-Butcher series and moving frames
• What is a classical r-matrix?
• Homology of generalized partition posets
• On the Hopf algebraic structure of Lie group integrators.
• Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras
• On the Butcher group and general multi-value methods
• On the set-theoretical Yang-Baxter equation
• Extension of the product of a post-Lie algebra and application to the SISO feedback transformation group
• Trees, renormalization and differential equations.
• A decomposition theorem for square-free unitary solutions of the quantum Yang-Baxter equation
• Set-theoretic solutions of the Yang-Baxter equation, braces and symmetric groups
• Lie-Butcher theory for Runge-Kutta methods
• Algebraic structures of B-series
• Set-theoretical solutions to the quantum Yang-Baxter equation
• Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
• Radical and weight of skew braces and their applications to structure groups of solutions of the Yang-Baxter equation
• Integration and geometrization of Rota-Baxter Lie algebras
• A new formula for Lazard's correspondence for finite braces and pre-Lie algebras
• Rota-Baxter groups, skew left braces, and the Yang-Baxter equation
• On the passage from finite braces to pre-Lie rings
• Post-symmetric braces and integration of post-Lie algebras
• Constructing finite simple solutions of the Yang-Baxter equation
• Factorizations of skew braces
• Post-Lie algebras and factorization theorems
• Braces and the Yang-Baxter equation
• Left-symmetric algebras, or pre-Lie algebras in geometry and physics
• Partition function of the eight-vertex lattice model
• Modules and Morita theorem for operads
• On the Lie enveloping algebra of a post-Lie algebra
• ENVELOPING ALGEBRAS OF PRELIE ALGEBRAS, SOLOMON IDEMPOTENTS AND THE MAGNUS FORMULA
• Skew braces and the Yang–Baxter equation
• On the Lie enveloping algebra of a pre-Lie algebra
• On some unsolved problems in quantum group theory
• On Engel groups, nilpotent groups, rings, braces and the Yang-Baxter equation
• On Structure Groups of Set-Theoretic Solutions to the Yang–Baxter Equation
• Skew left braces of nilpotent type
• Algebraic approach to Rump’s results on relations between braces and pre-lie algebras
• An Introduction to Pre‐Lie Algebras
• Functorial PBW theorems for post-Lie algebras
• The Magnus expansion and post-Lie algebras
• Crossed morphisms, integration of post-Lie algebras and the post-Lie Magnus expansion
• Relating Two Hopf Algebras Built from An Operad
• Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction
• An Algebraic Theory of Integration Methods