Some remarks on Lie bialgebra structures on simple complex Lie algebras

DOI10.1080/00927879908826696zbMath0957.17026OpenAlexW2158625325MaRDI QIDQ4262373

Alexander Stolin

Publication date: 2 May 2000

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927879908826696

zbMATH Keywords

Yang-Baxter equationroot systemLie bialgebra

Mathematics Subject Classification ID

Lie bialgebras; Lie coalgebras (17B62)

Related Items (14)

On the Classical Double of Parabolic Subalgebras ⋮ Structures of Malcev Bialgebras on a Simple Non-Lie Malcev Algebra ⋮ Classification of quantum groups and Belavin-Drinfeld cohomologies ⋮ Associative triples and the Yang-Baxter equation. ⋮ Quantum groups: from the Kulish-Reshetikhin discovery to classification ⋮ The 4th structure ⋮ Topological Lie bialgebras, Manin triples and their classification over \(gx\) ⋮ On Rota-Baxter operators of non-zero weight arisen from the solutions of the classical Yang-Baxter equation ⋮ Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation ⋮ Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras ⋮ New \(r\)-matrices for Lie bialgebra structures over polynomials ⋮ Lagrangian subalgebras and quasi-trigonometric \(r\)-matrices ⋮ Classification of quantum groups and Belavin–Drinfeld cohomologies for orthogonal and symplectic Lie algebras ⋮ Classification of quantum groups and Lie bialgebra structures on \(sl(n, \mathbb{F})\). Relations with Brauer group

Cites Work

• Quantum R-matrices and factorization problems
• On rational solutions of Yang-Baxter equations. Maximal orders in loop algebra
• Lie algebras graded by finite root systems and the intersection matrix algebras of Slodowy
• Boundary solutions of the classical Yang-Baxter equation
• New rational solutions of Yang-Baxter equation and deformed Yangians
• Lie algebras graded by finite root systems and intersection matrix algebras
• On Frobenius algebras and the quantum Yang-Baxter equation

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