Abstract
Let Γ be a finitely generated discrete group. The standard spectral triple on the group C ∗ -algebra C ∗ ( Γ ) 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 2 n of Wang. The quantum groups of orientation and real structure preserving isometries are also considered and the construction of the Laplacian for the standard spectral triple on C ∗ ( Γ ) is discussed.
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