C(SO_q(2n+1)/SO_q(2n-1)) as iterated torsioned quantum double suspensions of C(\mathbb{T})

Let ?? be a unital ?? ? -algebra, and let ? 2 ???? denote the ??-torsioned quantum double suspension of ??. For ?? ? (0, 1) and ?? ? 1, we prove that the ?? ? -algebra corresponding to the quotient space ?????? (2??+ 1)??????? (2??? 1) is isomorphic to ? 2(???1) ? 2 2 ? 2(???1)??(?? ). It follows as a consequence that these spaces are independent of the deformation parameter ?