EXAMPLE OF A GROUP WHOSE QUANTUM ISOMETRY GROUP DOES NOT DEPEND ON THE GENERATING SET

Abstract

AbstractIn this paper, we have shown that the quantum isometry group of Cr*(ℤ), denoted by ℚ(ℤ, S) as in Goswami and Mandal, Rev. Math. Phys.29(3) (2017), 1750008, 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 $\underbrace{\mathbb{Z} \times \mathbb{Z} \times\cdots \times \mathbb{Z}}_{n \ copies} \ \forall \ n>1$.