Generalization of the concept of classical \(r\)-matrix to Lie algebroids

DOI10.1016/j.geomphys.2021.104227zbMath1480.53103OpenAlexW3141366207MaRDI QIDQ2032683

Grzegorz Jakimowicz, Alina Dobrogowska

Publication date: 14 June 2021

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

Full work available at URL: https://doi.org/10.1016/j.geomphys.2021.104227

zbMATH Keywords

Lie algebraPoisson manifoldbi-Hamiltonian structureLie algebroidclassical \(r\)-matrixlifting of multivectors

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Deformation quantization, star products (53D55)

Related Items (2)

Eigenvalue problem versus Casimir functions for Lie algebras ⋮ A new look at Lie algebras

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Integrable Hamiltonian systems related to the Hilbert-Schmidt ideal
• What is a classical r-matrix?
• Pairs of compatible associative algebras, classical Yang-Baxter equation and quiver representations
• Compatible Lie brackets and the Yang-Baxter equation
• Completely integrable bi-Hamiltonian systems
• Lie bialgebroids and Poisson groupoids
• Compatible Poisson brackets on Lie algebras
• Bi-Hamiltonian structures on the tangent bundle to a Poisson manifold
• Deformation of the Poisson structure related to algebroid bracket of differential forms and application to real low dimentional Lie algebras
• Poisson manifolds, Lie algebroids, modular classes: a survey
• Poisson structures and their normal forms
• Vertical and horizontal lifts of multivector fields and applications
• Classification of Lie algebras with generic orbits of dimension 2 in the coadjoint representation
• On some deformations of the Poisson structure associated with the algebroid bracket of differential forms
• R-matrix, Lax pair, and multiparameter decompositions of Lie algebras
• ClassicalR-matrix theory for bi-Hamiltonian field systems
• Invariants of real low dimension Lie algebras
• A simple model of the integrable Hamiltonian equation
• Tangent lifts of Poisson and related structures
• Symplectic groupoids and Poisson manifolds
• Differential calculus on a Lie algebroid and Poisson manifolds
• Tangent Lie algebroids
• Tangent lifts of bi-Hamiltonian structures
• Classification and Identification of Lie Algebras
• Solutions of the classical Yang-Baxter equation for simple Lie algebras
• Quantum groupoids

This page was built for publication: Generalization of the concept of classical \(r\)-matrix to Lie algebroids