Existence of R-matrix for a quantized Kac–Moody algebra

DOI10.1017/S0305004100072510zbMath1009.17504OpenAlexW2050789418MaRDI QIDQ4314714

Volodimir Lyubashenko

Publication date: 5 May 2003

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0305004100072510

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Exactly solvable models; Bethe ansatz (82B23)

Cites Work

• q-Weyl group and a multiplicative formula for universal R-matrices
• Tortile Yang-Baxter operators in tensor categories
• Quantum Weyl group and a multiplicative formula for the R-matrix of a simple Lie algebra
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• On crystal bases of the \(q\)-analogue of universal enveloping algebras
• Universal \(R\)-matrix for quantized (super)algebras
• More examples of bicrossproduct and double cross product Hopf algebras
• Multiparameter quantum groups and twisted quasitriangular Hopf algebras
• Doubles of quasitriangular hopf algebras
• KILLING FORMS, HARISH-CHANDRA ISOMORPHISMS, AND UNIVERSAL R-MATRICES FOR QUANTUM ALGEBRAS

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