Quantum Isometry Groups of Group with Different Generating Sets

Abstract

The main goal of this paper is to discuss the structure of the quantum isometry groups associated to the discrete two matrix Z2-group G(2,Z2) and Dihedral group D8, and then we show that the quantum isometry groups Q(G(2,Z2)) of G(2,Z2) with two different generating sets are isomorphic to D(theta)(C*(D6), (delta)D6) := C*(D6 ⊕ D6), where (theta) is a automorphism of compact quantum group Q(G(2,Z2)). The quantum isometry group Q(D8) of D8 with the presentation (3) is not isomorphic to D(theta)(C*(D8), (delta)D8) except the case: One of D, D*,B and C is zero. But the quantum isometry group Q(D8) of with the presentation (4) is isomorphic to C*(D8 ⊕ D8).