Quantum Isometry Groups of Group with Different Generating Sets

Ji-cheng TAO


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).


Quantum isometry group, Generating set, Matrix Z2-group.


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