The quantum Heisenberg group H(1)q

DOI10.1063/1.529311zbMath0743.17016OpenAlexW2066146322MaRDI QIDQ3981676

Marco Tarlini, Riccardo Giachetti, Enrico Celeghini, Emanuele Sorace

Publication date: 26 June 1992

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

Full work available at URL: https://doi.org/10.1063/1.529311

zbMATH Keywords

contraction\(R\)-matrixLie algebra deformationsquantum enveloping Heisenberg algebraquantum matrix pseudogroups

Mathematics Subject Classification ID

Related Items (28)

Deformation quantization of the Heisenberg group ⋮ Contractions of the irreducible representations of the quantum algebras suq(2) and soq(3) ⋮ Free \(q\)-Schrödinger equation from homogeneous spaces of the 2-dim Euclidean quantum group ⋮ q-deformation of high-order Virasoro algebra ⋮ Quantum Heisenberg group and algebra: Contraction, left and right regular representations ⋮ The quantum two-dimensional Poincaré group from quantum group contraction ⋮ Classical deformations, Poisson–Lie contractions, and quantization of dual Lie bialgebras ⋮ Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra ⋮ Four-dimensional quantum affine algebras and space–time q-symmetries ⋮ Basic quantizations of \(D=4\) Euclidean, Lorentz, Kleinian and quaternionic \( {\mathfrak{o}}^{\star}(4) \) symmetries ⋮ Noncommutative relativistic spacetimes and worldlines from 2 + 1 quantum (anti-)de Sitter groups ⋮ Relativistic and Newtonian κ -space–times ⋮ Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras ⋮ Interpretation and extension of Green's ansatz for paraparticles ⋮ The contraction of SUμ(2) and its differential structures to Eκ(2) ⋮ Induced representations of quantum (1+1) Galilei algebras ⋮ Colored quantum universal enveloping algebras ⋮ Thermal field dynamics and bialgebras ⋮ The twisted Heisenberg algebra Uh,w(ℋ(4)) ⋮ Quantum \(SU(2)\) and \(E(2)\) groups. Contraction procedure ⋮ Quantum deformations of \(D =4\) Lorentz algebra revisited: Twistings of \(q\) -deformation ⋮ Quantum E(2) groups for complex deformation parameters ⋮ Deformation of noncommutative quantum mechanics ⋮ Quantum harmonic oscillator algebra and link invariants ⋮ Braid group representations from a deformation of the harmonic oscillator algebra ⋮ The \(\kappa \)-Newtonian and \(\kappa \)-Carrollian algebras and their noncommutative spacetimes ⋮ The \(\kappa\)-(A)dS noncommutative spacetime ⋮ The braided Heisenberg group

Cites Work

• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)_q
• INTRODUCTION TO THE YANG-BAXTER EQUATION
• Comment on the q-analogues of the harmonic oscillator
• Three-dimensional quantum groups from contractions of SU(2)q

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