QUANTUM 'ax + b' GROUP
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Publication:4420457
DOI10.1142/S0129055X02001405zbMath1042.46041MaRDI QIDQ4420457
Stanisław Lech Woronowicz, Stanislaw Zakrzewski
Publication date: 17 August 2003
Published in: Reviews in Mathematical Physics (Search for Journal in Brave)
Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89) Quantizations, deformations for selfadjoint operator algebras (46L65)
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The canonical central exact sequence for locally compact quantum groups ⋮ Extensions of locally compact quantum groups and the bicrossed product construction. ⋮ THE CLASSICAL LIMIT OF REPRESENTATION THEORY OF THE QUANTUM PLANE ⋮ NEW QUANTUM "az+b" GROUPS ⋮ Representation of the quantum plane, its quantum double, and harmonic analysis on \(GL_q^+(2,\mathbb{R })\) ⋮ Deformation of \(C^\ast\)-algebras by cocycles on locally compact quantum groups ⋮ A resolvent approach to the real quantum plane ⋮ From multiplicative unitaries to quantum groups. II ⋮ Non-existence of faithful isometric action of compact quantum groups on compact, connected Riemannian manifolds ⋮ Semidirect products of C*-quantum groups: multiplicative unitaries approach ⋮ A quantum \(GL(2,\mathbb{C})\) group at roots of unity ⋮ Quantum E(2) groups for complex deformation parameters ⋮ A C*-ALGEBRAIC FRAMEWORK FOR QUANTUM GROUPS ⋮ A new quantum deformation of `\(ax+b\)' group ⋮ Quantum \(\operatorname{GL}(2,\mathbb{C})\) group as double group over `\(az+b\)' quantum group
Cites Work
- Unbounded elements affiliated with \(C^*\)-algebras and non-compact quantum groups
- Operator theory in the \(C^*\)-algebra framework
- Integrable operator representations of \(\mathbb{R}_ q^ 2\), \(X_{q,\gamma}\) and \(SL_ q(2,\mathbb{R})\)
- QUANTUM EXPONENTIAL FUNCTION
- C*-ALGEBRAS GENERATED BY UNBOUNDED ELEMENTS
- FROM MULTIPLICATIVE UNITARIES TO QUANTUM GROUPS
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