Quantum \(\operatorname{GL}(2,\mathbb{C})\) group as double group over `\(az+b\)' quantum group
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Publication:1611478
DOI10.1016/S0034-4877(02)80008-8zbMath1057.46059MaRDI QIDQ1611478
Publication date: 2002
Published in: Reports on Mathematical Physics (Search for Journal in Brave)
quantum group\(C^*\)-algebraHilbert spacerepresentationunbounded operatorlocally compact groupHopf *-algebraquantum exponential function
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)
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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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- 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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