The Haar measure on finite quantum groups

DOI10.1090/S0002-9939-97-04037-9zbMath0888.16023MaRDI QIDQ4372445

Alfons Van Daele

Publication date: 11 December 1997

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

existenceuniquenessantipodescounitsquantum groupsGaussian polynomialsfinite-dimensional Hopf algebrasleft integralsfinite-dimensional complex Hopf algebrasright integrals

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37)

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Cites Work

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• Compact matrix pseudogroups
• Quantum \(SU(2)\) and \(E(2)\) groups. Contraction procedure
• Discrete quantum groups
• Derivations of simple \(C^ *\)-algebras. III
• Unitaires multiplicatifs et dualité pour les produits croisés de $\mathrm{C}^*$-algèbres
• Dual Pairs of Hopf *-Algebras
• DISCRETE QUANTUM GROUPS I: THE HAAR MEASURE