Example of a Group Whose Quantum Isometry Group Does Not Depend on the Generating Set

Abstract

In this article we have shown that the quantum isometry group of C * r (Z), denoted by Q(Z, S) as in [16], with respect to a symmetric generating set S does not depend on the generating set S. Moreover, we have proved that the result is no longer true if the group Z is replaced by Z × Z × · · · × Z n copies for n > 1.