On actions of compact quantum groups

zbMath1272.46054arXivmath/0701033MaRDI QIDQ351816

Piotr M. Sołtan

Publication date: 10 July 2013

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701033

zbMATH Keywords

actioncompact quantum groupPodleś algebraic core

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Noncommutative geometry in quantum theory (81R60) Quantum groups (quantized function algebras) and their representations (20G42) Quantizations, deformations for selfadjoint operator algebras (46L65)

Related Items (12)

A covariant Stinespring theorem ⋮ Liberation theory for noncommutative homogeneous spaces ⋮ Free actions of compact quantum groups on unital \(C^\ast\)-algebras ⋮ Faithful compact quantum group actions on connected compact metrizable spaces ⋮ Convergence of Fourier truncations for compact quantum groups and finitely generated groups ⋮ A note on the injectivity of actions of compact quantum groups on a class of $C^{\ast }$-algebras ⋮ Quantum group of automorphisms of a finite quantum group ⋮ Pullbacks and nontriviality of associated noncommutative vector bundles ⋮ Liberations and twists of real and complex spheres ⋮ Quantum automorphism groups of finite quantum groups are classical ⋮ Integration over the quantum diagonal subgroup and associated Fourier-like algebras ⋮ Existence and examples of quantum isometry groups for a class of compact metric spaces

Cites Work

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• Compact quantum metric spaces and ergodic actions of compact quantum groups
• Ergodic actions of universal quantum groups on operator algebras
• Symmetries of quantum spaces. Subgroups and quotient spaces of quantum \(SU(2)\) and \(SO(3)\) groups
• Quantum \(\mathrm{SO}(3)\) groups and quantum group actions on \(M_{2}\)
• Approximation properties and entropy estimates for crossed products by actions of amenable discrete quantum groups
• Introduction to Quantum Groups
• Theory of operator algebras I.
• Co-amenability of compact quantum groups

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