An algebraic framework for group duality
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Publication:1281891
DOI10.1006/aima.1998.1775zbMath0933.16043OpenAlexW2170835830MaRDI QIDQ1281891
Publication date: 20 January 2000
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/aima.1998.1775
dualitiesintegralscompact quantum groupsAbelian groupslinear functionalsinvariant functionalsmultiplier Hopf algebrasdiscrete quantum groups
Quantum groups (quantized enveloping algebras) and related deformations (17B37) Homomorphisms and multipliers of function spaces on groups, semigroups, etc. (43A22) Duality theorems for locally compact groups (22D35) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Quantum deformation of Lorentz group
- Compact matrix pseudogroups
- Quantum \(SU(2)\) and \(E(2)\) groups. Contraction procedure
- Multiplier Hopf algebras of discrete type
- CQG algebras: A direct algebraic approach to compact quantum groups
- A von Neumann algebra framework for the duality of the quantum groups
- Discrete quantum groups
- Actions of multiplier hopf algebras
- Dual Pairs of Hopf *-Algebras
- Multiplier Hopf Algebras
- DISCRETE QUANTUM GROUPS I: THE HAAR MEASURE
- The Haar measure on finite quantum groups
- C*-Algebraic Quantum Groups Arising from Algebraic Quantum Groups
- The Haar Measure on a Compact Quantum Group
- Pairing and quantum double of multiplier Hopf algebras