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arXiv · 1002.2551

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

Jyotishman Bhowmick·Adam Skalski
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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.

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BibTeXRIS

Jyotishman Bhowmick, Adam Skalski. 2010-02-12. Quantum isometry groups of noncommutative manifolds associated to group C*-algebras. https://doi.org/10.1016/j.geomphys.2010.05.007

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