Lagrangian subalgebras and quasi-trigonometric \(r\)-matrices

DOI10.1007/S11005-008-0264-5zbMath1243.17015OpenAlexW2055928161MaRDI QIDQ1013616

Iulia Pop, Alexander Stolin

Publication date: 20 April 2009

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11005-008-0264-5

zbMATH Keywords

classical Yang-Baxter equationparabolic subalgebra\(r\)-matrixManin triplegeneralized Belavin-Drinfeld data

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Lie bialgebras; Lie coalgebras (17B62)

Related Items (6)

Classification of Lie bialgebras over current algebras ⋮ Simple vector bundles on a nodal Weierstrass cubic and quasi-trigonometric solutions of the classical Yang–Baxter equation ⋮ Topological Lie bialgebras, Manin triples and their classification over \(gx\) ⋮ On the General Classification of Lie Bialgebra Structures over Polynomials ⋮ Classification of classical twists of the standard Lie bialgebra structure on a loop algebra ⋮ New \(r\)-matrices for Lie bialgebra structures over polynomials

Cites Work

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• Formality theorem for Lie bialgebras and quantization of twists and coboundary \(r\)-matrices
• The 4th structure
• On some Lie bialgebra structures on polynomial algebras and their quantization
• Quantum R matrix for the generalized Toda system
• On rational solutions of Yang-Baxter equations. Maximal orders in loop algebra
• Universal \(R\)-matrix for quantized (super)algebras
• Some remarks on Lie bialgebra structures on simple complex Lie algebras
• Classification of Manin triples for complex reductive Lie algebras. (With an appendix by Guillaume Macey)

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