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

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

2010-02-12

arxiv.org/abs/1002.2551v2

Mathematics

Operator Algebras

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

Scientific paper

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.

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