Representations of the q-deformed algebra Uq′(so4)

DOI10.1063/1.1402631zbMath1017.81025arXivmath/0102036OpenAlexW1611527972MaRDI QIDQ2774736

A. U. Klimyk, Miloslav Havlíček, Severin Pošta

Publication date: 26 February 2002

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

Full work available at URL: https://arxiv.org/abs/math/0102036

zbMATH Keywords

quantum gravityalgebraic topologyDrinfeld-Jimbo quantum algebraproducts of irreducible representations

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) Quantization of the gravitational field (83C45) Operator algebra methods applied to problems in quantum theory (81R15)

Related Items (3)

Affine symmetries of orbit polytopes ⋮ On representations of $U’_q\mathfrak {so}_n$ ⋮ The \(q\)-Higgs and Askey-Wilson algebras

Cites Work

• \(q\)-deformed orthogonal and pseudo-orthogonal algebras and their representations
• Invariants of \(2+1\) gravity
• Nonstandard \(U_q(\text{so}_3)\) and \(U_q(\text{so}_4)\): Tensor products of representations, oscillator realizations and roots of unity
• Macdonald's symmetric polynomials as zonal spherical functions on some quantum homogeneous spaces
• Observables in 3D gravity and geodesic algebras.
• Representations of the nonstandard (twisted) deformation \(U'_q(\text{so}_n)\) for \(q\) a root of unity.
• Spectra, eigenvectors and overlap functions for representation operators of \(q\)-deformed algebras
• The representations of \(U_ q (\text{so}_ 4)\) and \(U_ q (\text{so}_{3,1})\)
• On the classification of irreducible finite-dimensional representations of Uq′(so3) algebra
• The q-Laplace operator and q-harmonic polynomials on the quantum vector space
• Quantum deformations of SU(2)
• Multiplicative structure of Kauffman bracket skein module quantizations
• Representations of the cyclically symmetric q-deformed algebra soq(3)
• Representations of the q-deformed algebra U_q'(SO₄)
• Central elements of the algebras \(U'_q(\text{so}_m)\) and \(U_q(\text{iso}_m)\)
• Nonclassical type representations of the \(q\)-deformed algebra \(U_q'(\text{so}_n)\)

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