The \(R\)-matrix presentation for the rational form of a quantized enveloping algebra

DOI10.1016/j.jalgebra.2024.02.024arXiv2306.09971OpenAlexW4392359752MaRDI QIDQ6203780

Curtis Wendlandt, Matthew Rupert

Publication date: 8 April 2024

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

Full work available at URL: https://arxiv.org/abs/2306.09971

zbMATH Keywords

quantum groupsquantum algebrasYang-Baxter equationssemisimple Lie algebrasquantized enveloping algebrasR-matrices

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Yang-Baxter equations and Rota-Baxter operators (17B38)

Cites Work

• q-Weyl group and a multiplicative formula for universal R-matrices
• Some applications of the quantum Weyl groups
• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• Isomorphism of two realizations of quantum affine algebra \(U_ q(\widehat{\mathfrak{gl}}(n))\)
• The \(R\)-matrix presentation for the Yangian of a simple Lie algebra
• Isomorphism between the \(R\)-matrix and Drinfeld presentations of quantum affine algebra: types \(B\) and \(D\)
• Shifted quantum affine algebras: integral forms in type \(A\)
• Vertex representations for Yangians of Kac-Moody algebras
• L operators and Drinfeld’s generators
• Quantization of Lie group and algebra of G2 type in the Faddeev–Reshetikhin–Takhtajan approach
• Isomorphism between the R-matrix and Drinfeld presentations of quantum affine algebra: Type C
• Elementary Bialgebra Properties of Group Rings and Enveloping Rings: An Introduction to Hopf Algebras
• Introduction to Lie Algebras and Representation Theory
• Introduction to quantum groups
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