Equitable presentations for multiparameter quantum groups

DOI10.1007/s10114-021-0676-zzbMath1501.17011OpenAlexW3206626159MaRDI QIDQ2244672

Jiao Zhang, Yufeng Pei, Hu, Naihong

Publication date: 12 November 2021

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-021-0676-z

zbMATH Keywords

Hopf algebrasquantum groupsequitable presentation

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) Quantum groups (quantized function algebras) and their representations (20G42)

Cites Work

• Pointed Hopf algebras with triangular decomposition. A characterization of multiparameter quantum groups
• The universal Askey-Wilson algebra and the equitable presentation of \(U_{q}(sl_{2})\)
• The equitable basis for \({\mathfrak{sl}_2}\)
• Complete reducibility theorems for modules over pointed Hopf algebras.
• A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems.
• The equitable presentation of \(\mathfrak{osp}_q(1|2)\) and a \(q\)-analog of the Bannai-Ito algebra
• Notes on 2-parameter quantum groups. I.
• Lusztig isomorphisms for Drinfel'd doubles of bosonizations of Nichols algebras of diagonal type
• On the classification of finite-dimensional pointed Hopf algebras.
• Quantum groups and quantum shuffles
• Algebraic structure of multiparameter quantum groups
• Centers of generalized quantum groups
• Two-parameter quantum groups and Drinfel'd doubles.
• Irreducible modules for the quantum affine algebra \(U_{q}(\mathfrak {\widehat{sl}_2})\) and its Borel subalgebra
• The two parameter quantum groups \(U_{r, s} (\mathfrak g)\) associated to generalized Kac-Moody algebra and their equitable presentation
• Tridiagonal pairs and the quantum affine algebra \(U_q(\widehat{\text{sl}}_2)\).
• Irreducible modules for the quantum affine algebra \(U_{q}(\mathfrak g)\) and its Borel subalgebra \(U_{q}(\mathfrak g)^{\geqslant 0}\)
• The Weyl groupoid of a Nichols algebra of diagonal type
• The quantum algebra \(U_q(\mathfrak{sl}_2)\) and its equitable presentation
• The equitable presentation for the quantum group associated with a symmetrizable Kac-Moody algebra
• Drinfel'd doubles and Lusztig's symmetries of two-parameter quantum groups
• Finite-dimensional irreducible \(U_q(\mathfrak{sl}_2)\)-modules from the equitable point of view
• Multiparameter quantum groups and twisted quasitriangular Hopf algebras
• DOUBLE LOOP QUANTUM ENVELOPING ALGEBRAS
• On Nichols algebras of diagonal type
• Multi-parameter Quantum Groups and Quantum Shuffles, (I)
• Notes on Two-Parameter Quantum Groups, (II)
• Multiparameter quantum groups, bosonizations and cocycle deformations
• A characterization of quantum groups
• The R-matrix of quantum doubles of Nichols algebras of diagonal type
• Drinfel'd doubles and Shapovalov determinants
• Kostant-Lusztig 𝔸-bases of multiparameter quantum groups

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