Q rotations and other Q transformations as unitary nonlinear automorphisms of quantum algebras

DOI10.1063/1.530088zbMath0789.17011OpenAlexW2046933508MaRDI QIDQ4203238

Alexei Zhedanov

Publication date: 8 September 1993

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.530088

zbMATH Keywords

quantum algebrasunitary operator\(q\)-coherent statesAskey-Wilson polynomialnonlinear automorphisms

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) Applications of Lie (super)algebras to physics, etc. (17B81) Coherent states (81R30)

Related Items (5)

\(q\)-rotations and Krawtchouk polynomials ⋮ An algebraic interpretation of the \(q\)-Meixner polynomials ⋮ Even and odd \(q\)-coherent states in a finite-dimensional basis and their squeezing properties ⋮ An algebraic interpretation of the multivariate \(q\)-Krawtchouk polynomials ⋮ SU q (3) corepresentations and bivariate q-Krawtchouk polynomials

Cites Work

• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Poisson manifolds and the Schouten bracket
• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• On coherent states for the simplest quantum groups
• Lie algebras and recurrence relations. III: \(q\)-analogs and quantized algebras
• On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)_q
• On the q oscillator and the quantum algebra su_q(1,1)
• Quantum algebra deforming maps, Clebsch–Gordan coefficients, coproducts, R and U matrices
• Nonlinear shifts of q-Bose operators and q-coherent states

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