Quantum isometry groups of noncommutative manifolds associated to group C*-algebras

Abstract

Let G be a finitely generated discrete group. The standard spectral triple on the group C*-algebra C*(G) is shown to admit the quantum group of orientation preserving isometries. This leads to new examples of compact quantum groups. In particular the quantum isometry group of the C*-algebra of the free group on n-generators is computed and turns out to be a quantum group extension of the quantum permutation group A_{2n} of Wang. The quantum groups of orientation and real structure preserving isometries are also considered and construction of the Laplacian for the standard spectral triple on C*(G) discussed.

23 pages, v2 corrects a few misprints and adds more explanatory remarks. The paper will appear in the Journal of Geometry and Physics

References in corpus (6)

• The hyperoctahedral quantum group
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• Quantum Isometry Group for Spectral Triples with Real Structure
• Quantum Isometry Groups of 0- Dimensional Manifolds
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Cited by in corpus (11)

• Quantum symmetry groups of C*-algebras equipped with orthogonal filtrations
• Quantum Isometries of the finite noncommutative geometry of the Standard Model
• Quantum isometry groups of symmetric groups
• Lévy Processes on Quantum Permutation Groups
• Quantum automorphism groups of connected locally finite graphs and quantizations of discrete groups
• Quantum symmetries of the twisted tensor products of C*-algebras
• Quantum Isometry group of dual of finitely generated discrete groups and quantum groups
• Existence and rigidity of quantum isometry groups for compact metric spaces
• Quantum isometry group of dual of finitely generated discrete groups- $\text{II}$
• Isometric coactions of compact quantum groups on compact quantum metric spaces
• Projective limits of quantum symmetry groups and the doubling construction for Hopf algebras