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

Abstract

Let $A$ be a unital $C^*$-algebra, and let $\Sigma^2_m A$ denote the $m$-torsioned quantum double suspension of $A$. For $q \in (0,1)$ and $n \geq 1$, we prove that the $C^*$-algebra corresponding to the quotient space $SO_q(2n+1)/SO_q(2n-1)$ is isomorphic to $\Sigma^{2(n-1)} \, \Sigma^2_2 \, \Sigma^{2(n-1)} C(\mathbb{T})$. It follows as a consequence that these spaces are independent of the deformation parameter $q$.