QUANTUM ISOMETRY GROUPS OF SYMMETRIC GROUPS

DOI10.1142/S0129167X12500747zbMath1279.58003arXiv1107.1657OpenAlexW3099914360MaRDI QIDQ2909470

Jan Liszka-Dalecki, Piotr M. Sołtan

Publication date: 30 August 2012

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

Full work available at URL: https://arxiv.org/abs/1107.1657

zbMATH Keywords

semisimple Hopf algebrasquantum groupsspectral triplesquantum isometry groupsmultiplier Hopf algebras

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) (C^*)-algebras and (W^*)-algebras in relation to group representations (22D25) Geometry of quantum groups (58B32) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89) Quantizations, deformations for selfadjoint operator algebras (46L65) Hopf algebras and their applications (16T05)

Related Items (11)

EXAMPLE OF A GROUP WHOSE QUANTUM ISOMETRY GROUP DOES NOT DEPEND ON THE GENERATING SET ⋮ A duality principle for noncommutative cubes and spheres ⋮ Non-existence of genuine (compact) quantum symmetries of compact, connected smooth manifolds ⋮ Quantum isometry groups for dihedral group \(D_{2(2n+1)}\) ⋮ Quantum isometries and group dual subgroups ⋮ Quantum isometry groups of dual of finitely generated discrete groups and quantum groups ⋮ Unnamed Item ⋮ Existence and rigidity of quantum isometry groups for compact metric spaces ⋮ Quantum isometry group of dual of finitely generated discrete groups. II. ⋮ Non-existence of faithful isometric action of compact quantum groups on compact, connected Riemannian manifolds ⋮ Operator algebras in India in the past decade

Cites Work

• Two-parameter families of quantum symmetry groups
• Quantum group of isometries in classical and noncommutative geometry
• Quantum group of orientation-preserving Riemannian isometries
• Quantum deformation of Lorentz group
• Quantum isometry groups of the Podles spheres
• Quantum isometry groups of noncommutative manifolds associated to group \(C^{*}\)-algebras
• Quantum families of maps and quantum semigroups on finite quantum spaces
• Unbounded elements affiliated with \(C^*\)-algebras and non-compact quantum groups
• An algebraic framework for group duality
• Symmetries of quantum spaces. Subgroups and quotient spaces of quantum \(SU(2)\) and \(SO(3)\) groups
• Quantum isometry groups: Examples and computations
• ON QUANTUM SEMIGROUP ACTIONS ON FINITE QUANTUM SPACES
• Introduction to Quantum Groups
• Actions of multiplier hopf algebras
• C*-Algebraic Quantum Groups Arising from Algebraic Quantum Groups

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