The quantized universal enveloping algebras Uq(iso(N)), Uq(e(3,1)) and Uq(e(N)) and the representation theory of Uq(e(3))

DOI10.1063/1.532231zbMath0897.17019OpenAlexW149276542MaRDI QIDQ4384801

Ralf Weixler, Sebastian Sachse

Publication date: 12 October 1998

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

Full work available at URL: https://doi.org/10.1063/1.532231

zbMATH Keywords

Hopf algebrasirreducible representationsquantized universal enveloping algebrasfunction algebras*-involutionsquantized Euclidean algebras

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) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89)

Cites Work

• Compact matrix pseudogroups
• Bicovariant differential calculus on quantum groups \(SU_ q(N)\) and \(SO_ q(N)\)
• Quantum \(E(2)\) group and its Pontryagin dual
• \(q\)-deformed Poincaré algebra
• Cross products by braided groups and bosonization
• Integrable operator representations of \(\mathbb{R}_ q^ 2\), \(X_{q,\gamma}\) and \(SL_ q(2,\mathbb{R})\)
• Irreducible unitary representations of quantum Lorentz group
• Braided bosonization and inhomogeneous quantum groups
• Inhomogeneous quantum groups and their quantized universal enveloping algebras
• THE q-EUCLIDEAN ALGEBRA U_q(e^N) AND THE CORRESPONDING q-EUCLIDEAN LATTICE
• A QUANTUM LORENTZ GROUP
• Wigner-Eckart theorem for the quantum group U_q(n)
• Inhomogeneous quantum groups
• ISO q (3) and ISO q(2,1)
• Irreducible tensor operators in the regular coaction formalisms of compact quantum group algebras

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