ELEMENTARY PARABOLIC TWIST

DOI10.1142/S0219498802000306zbMath1022.17012arXivmath/0107034OpenAlexW2963322157MaRDI QIDQ4416616

M. E. Samsonov, Vladimir D. Lyakhovskiĭ

Publication date: 3 August 2003

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0107034

zbMATH Keywords

quantum algebrassimple Lie algebrasHopf algebra deformationsminimal parabolic subalgebratwist deformationsextended Jordanian twistparabolic twistuniversal \(\mathcal R\)-matrix

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups (quantized function algebras) and their representations (20G42)

Related Items (6)

Minimal parabolic quantum groups in twist deformations ⋮ Quantum groups and deformation quantization: Explicit approaches and implicit aspects ⋮ Parabolic twists for the linear algebras \(A_{n-1}\) ⋮ Quantum duality in quantum deformations ⋮ Semi-classical twists for \(\mathfrak{sl}_3\) and \(\mathfrak{sl}_4\) boundary \(r\)-matrices of Cremmer-Gervais type ⋮ From dynamical to non-dynamical twists

Cites Work

• The quantum group structure associated with non-linearly extended Virasoro algebras
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Universal \(R\)-matrix for esoteric quantum groups
• Boundary solutions of the classical Yang-Baxter equation
• Quantization of Lie bialgebras. I
• Universal exponential solution of the Yang-Baxter equation
• Multiparameter quantum groups and twisted quasitriangular Hopf algebras
• Extended Jordanian twists for Lie algebras
• Jordanian twists on deformed carrier subspaces
• Chains of twists for classical Lie algebras
• Peripheric extended twists

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