The \(\mathbb{Z}_3\)-symmetric down-up algebra

DOI10.1016/J.JALGEBRA.2023.09.039MaRDI QIDQ6565668

Paul Terwilliger

Publication date: 2 July 2024

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

zbMATH Keywords

Weyl algebraKac-Moody Lie algebraloop algebradown-up algebra

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Canonical forms, reductions, classification (15A21) Ring-theoretic aspects of quantum groups (16T20)

Cites Work

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• The algebra \(U_q(\mathfrak{sl}_2)\) in disguise
• Billiard arrays and finite-dimensional irreducible \(U_q(\mathfrak{sl}_2)\)-modules
• The universal Askey-Wilson algebra and the equitable presentation of \(U_{q}(sl_{2})\)
• Lowering-raising triples and \(U_q(\mathfrak{sl}_2)\)
• Bidiagonal triples
• The equitable basis for \({\mathfrak{sl}_2}\)
• The diamond lemma for ring theory
• Down-up algebras
• Centers of down-up algebras
• Down-up algebras and their representation theory
• Down-up algebras and ambiskew polynomial rings
• Hopf down-up algebras.
• Two-parameter quantum groups and Drinfel'd doubles.
• Basic properties of generalized down-up algebras.
• Dual polar graphs, the quantum algebra \(U_q(\mathfrak{sl}_{2})\), and Leonard systems of dual \(q\)-Krawtchouk 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
• Finite-dimensional irreducible \(U_q(\mathfrak{sl}_2)\)-modules from the equitable point of view
• Lie superalgebras and enveloping algebras
• Primitive Ideals of Noetherian Down-Up Algebras
• Whittaker modules for generalized Weyl algebras
• INJECTIVE MODULES OVER DOWN-UP ALGEBRAS
• Automorphisms of Generalized Down-Up Algebras
• Differential Posets
• Noetherian down-up algebras
• CENTERS OF DOWN-UP ALGEBRAS OVER FIELDS OF PRIME CHARACTERISTIC
• The Lusztig automorphism of Uq(𝔰𝔩2) from the equitable point of view
• PRIMITIVE IDEALS OF NON-NOETHERIAN DOWN-UP ALGEBRAS
• BIDIAGONAL PAIRS, THE LIE ALGEBRA 𝔰𝔩₂, AND THE QUANTUM GROUP U_q(𝔰𝔩₂)
• Gems from the Work of Georgia Benkart
• Sur les algèbres de Weyl
• A Hopf structure for down-up algebras
• Down-up algebras and their representations.

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