Quantizations \(U_q (\mathfrak{sl}_{n + 1}^+)\) and \(U_q (\mathfrak{so}_{2n + 1}^+)\) as quadratic-linear algebras

DOI10.1016/j.jalgebra.2020.08.009zbMath1468.17023OpenAlexW3082344653MaRDI QIDQ2201076

Vladislav Kharchenko

Publication date: 25 September 2020

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2020.08.009

zbMATH Keywords

Hopf algebraKoszul algebrasPBW-basisGröbner-Shirshov relations

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Ring-theoretic aspects of quantum groups (16T20) Hopf algebras and their applications (16T05) Gröbner-Shirshov bases (16Z10)

Cites Work

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• Quantum Lie theory. A multilinear approach
• Some remarks on Koszul algebras and quantum groups
• Right coideal subalgebras of \(U_q^+(\mathfrak{so}_{2n+1})\)
• Gröbner-Shirshov bases for quantum enveloping algebras
• A combinatorial approach to the quantification of Lie algebras.
• An analogue of P.B.W. theorem and the universal R-matrix for \(U_ h\mathfrak{sl}(N+1)\)
• A Poincaré-Birkhoff-Witt theorem for quantized universal enveloping algebras of type \(A_ N\)
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Two-parameter quantum groups and Drinfel'd doubles.
• Right coideal subalgebras in \(U_q(\mathfrak{sl}_{n+1})\)
• Drinfel'd doubles and Lusztig's symmetries of two-parameter quantum groups
• Multiparameter quantum groups and twisted quasitriangular Hopf algebras
• Quantum double and multiparameter quantum groups
• Koszul Resolutions
• On Burnside's Problem

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