TOPOLOGICAL INVARIANCE OF QUANTUM QUATERNION SPHERES

The C*-algebra of continuous functions on the quantum quaternion sphere H-q(2n) can be identified with the quotient algebra C(SPq(2n)/SPq(2n-2)). In the commutative case, i.e., for q=1, the topological space SP(2n)/SP(2n-2) is homeomorphic to the odd-dimensional sphere S4n-1. In this paper, we prove the noncommutative analogue of this result. Using homogeneous C*-extension theory, we prove that the C*-algebra C(H-q(2n)) is isomorphic to the C*-algebra C(S-q(4n-1)). This further implies that for different values of q in [0,1), the C*-algebras underlying the noncommutative spaces H-q(2n) are isomorphic.