The contraction of SUμ(2) and its differential structures to Eκ(2)

DOI10.1063/1.533297zbMath0987.81041arXivmath/9807005OpenAlexW1612388629MaRDI QIDQ2737999

Pawel Maslanka, Piotr Kosiński

Publication date: 30 August 2001

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

Full work available at URL: https://arxiv.org/abs/math/9807005

zbMATH Keywords

differential calculideformed Euclidean groupfour-dimensionalthree-dimensional left covariant calculus

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) Noncommutative geometry in quantum theory (81R60) Geometry of quantum groups (58B32)

Cites Work

• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• Bicovariant differential calculi on \(S_ \mu U(2)\)
• Differential calculus on compact matrix pseudogroups (quantum groups)
• New quantum Poincaré algebra and \(\kappa\)-deformed field theory
• 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
• The quantum two-dimensional Poincaré group from quantum group contraction
• The gamma -Poincare quantum group from quantum group contraction
• An R-matrix approach to the quantization of the Euclidean group E(2)
• Three-dimensional quantum groups from contractions of SU(2)q

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