Quantum Isometry Groups of 0- Dimensional Manifolds

Details Quantum Isometry Groups of 0- Dimensional Manifolds Quantum Isometry Groups of 0- Dimensional Manifolds

2008-07-27

arxiv.org/abs/0807.4288v2

Mathematics

Operator Algebras

typos corrected, To appear in Trans.AMS

Scientific paper

Quantum isometry groups of spectral triples associated with approximately finite-dimensional C*-algebras are shown to arise as inductive limits of quantum symmetry groups of corresponding truncated Bratteli diagrams. This is used to determine explicitly the quantum isometry group of the natural spectral triple on the algebra of continuous functions on the middlethird Cantor set. It is also shown that the quantum symmetry groups of finite graphs or metric spaces coincide with the quantum isometry groups of the corresponding classical objects equipped with natural Laplacians.

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