Quantum \(\operatorname{GL}(2,\mathbb{C})\) group as double group over `\(az+b\)' quantum group

DOI10.1016/S0034-4877(02)80008-8zbMath1057.46059MaRDI QIDQ1611478

Wiesław Pusz

Publication date: 2002

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

quantum group\(C^*\)-algebraHilbert spacerepresentationunbounded operatorlocally compact groupHopf *-algebraquantum exponential function

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)

Related Items

THE CLASSICAL LIMIT OF REPRESENTATION THEORY OF THE QUANTUM PLANE ⋮ Representation of the quantum plane, its quantum double, and harmonic analysis on \(GL_q^+(2,\mathbb{R })\) ⋮ Gauss-Lusztig decomposition for positive quantum groups and representation by \(q\)-tori ⋮ Hopf images in locally compact quantum groups

Cites Work

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• Quantum deformation of Lorentz group
• Unbounded elements affiliated with \(C^*\)-algebras and non-compact quantum groups
• Quantum Lorentz group having Gauss decomposition property
• REPRESENTATIONS OF QUANTUM LORENTZ GROUP ON GELFAND SPACES
• QUANTUM 'ax + b' GROUP
• QUANTUM EXPONENTIAL FUNCTION
• QUANTUM 'az + b' GROUP ON COMPLEX PLANE
• C*-ALGEBRAS GENERATED BY UNBOUNDED ELEMENTS
• FROM MULTIPLICATIVE UNITARIES TO QUANTUM GROUPS
• Quantum groups
• A quantum \(GL(2,\mathbb{C})\) group at roots of unity

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