Extended commutator algebra for the \(q\)-oscillator and a related Askey-Wilson algebra
type: Item
instance of: scholarly article
title: Extended commutator algebra for the \(q\)-oscillator and a related Askey-Wilson algebra
author: Rafael Reno S. Cantuba
published in: Communications in Mathematics
publication date: 2024-08-23T00:00:00Z
Mathematics Subject Classification ID: 47L30
Mathematics Subject Classification ID: 17B60
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 16S15
Mathematics Subject Classification ID: 81R50
zbMATH DE Number: 7900708
zbMATH Keywords: \(q\)-oscillator
zbMATH Keywords: deformed commutation relations
zbMATH Keywords: commutator algebra
zbMATH Keywords: Lie algebra
zbMATH Keywords: commutator of operators
zbMATH Keywords: Lie polynomial
zbMATH Keywords: creation operator
zbMATH Keywords: annihilation operator
zbMATH Keywords: number operator
zbMATH Keywords: Askey-Wilson algebra
MaRDI profile type: Publication
cites work: Hilbert spaces of analytic functions and generalized coherent states
cites work: RLC circuit realization of a q-deformed harmonic oscillator with time dependent mass
cites work: The diamond lemma for ring theory
cites work: The quantum group SUq(2) and a q-analogue of the boson operators
cites work: Lie polynomials in \(q\)-deformed Heisenberg algebras
cites work: Compactness property of Lie polynomials in the creation and annihilation operators of the \(q\)-oscillator
cites work: Lie polynomials in an algebra defined by a linearly twisted commutation relation
cites work: An extension of a \(q\)-deformed Heisenberg algebra and its Lie polynomials
cites work: Lie polynomial characterization problems
cites work: Torsion-type \(q\)-deformed Heisenberg algebra and its Lie polynomials
cites work: On position and momentum operators in the q-oscillator algebra
cites work: Algebraic curves for commuting elements in the \(q\)-deformed Heisenberg algebra
cites work: Q5472809
cites work: Q4516129
cites work: Two-sided ideals in \(q\)-deformed Heisenberg algebras.
cites work: Finite-dimensional irreducible modules of the universal Askey-Wilson algebra
cites work: Lax Matrices for Yang-Baxter Maps
cites work: Non-Noetherian generalized Heisenberg algebras
cites work: Quantum generalized Heisenberg algebras and their representations
cites work: Structure and isomorphisms of quantum generalized Heisenberg algebras
cites work: Simple weight modules over weak generalized Weyl algebras.
cites work: Finite-dimensional simple modules over generalized Heisenberg algebras
cites work: On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)q
cites work: Integrable operator representations of \(\mathbb{R}_ q^ 2\), \(X_{q,\gamma}\) and \(SL_ q(2,\mathbb{R})\)
cites work: The universal Askey-Wilson algebra
cites work: ``Hidden symmetry'' of Askey-Wilson polynomials
DOI: 10.46298/CM.10820
description: scientific article; zbMATH DE number 7900708