Classical deformations, Poisson–Lie contractions, and quantization of dual Lie bialgebras

DOI10.1063/1.531331zbMath0824.58027OpenAlexW2068595790MaRDI QIDQ4837375

Mariano Santander, Ángel Ballesteros, Mariano A. del Olmo, Francisco J. Herranz

Publication date: 16 November 1995

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

Full work available at URL: https://doi.org/10.1063/1.531331

zbMATH Keywords

deformationsquantizationPoisson-Hopf algebraPoisson-Lie contractions

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) Geometric quantization (53D50)

Related Items

AdS Poisson homogeneous spaces and Drinfel’d doubles ⋮ Noncommutative relativistic spacetimes and worldlines from 2 + 1 quantum (anti-)de Sitter groups ⋮ Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras ⋮ Curvature from quantum deformations ⋮ The \(\kappa \)-Newtonian and \(\kappa \)-Carrollian algebras and their noncommutative spacetimes ⋮ Coisotropic Lie bialgebras and complementary dual Poisson homogeneous spaces

Cites Work

• The dual of a quantum group
• The quantum Heisenberg group H(1)q
• The three-dimensional Euclidean quantum group E(3)q and its R-matrix
• The E q(2) group via direct quantization of the Lie–Poisson structure and its Lie algebra
• Quantum structure of the motion groups of the two-dimensional Cayley-Klein geometries
• Quantum Heisenberg group
• An R-matrix approach to the quantization of the Euclidean group E(2)
• Quantum Poincare group related to the kappa -Poincare algebra
• A universal non-quasitriangular quantization of the Heisenberg group