The structure of quantum spheres

We show that the C*-algebra $C\left(\mathbb{S} _{q}^{2n+1}\right)$ of a quantum sphere $\mathbb{S} _{q}^{2n+1}$, $q>1$, consists of continuous fields $\left\{f_{t}\right\}_{t\in\mathbb{T} }$ of operators $f_{t}$ in a C*-algebra $\mathcal{A}$, which contains the algebra $\mathcal{K}$ of compact operators with $\mathcal{A}/\mathcal{K}\cong C\left( \mathbb{S} _{q} ^{2n-1}\right)$, such that $\rho_{\ast}\left( f_{t}\right)$ is a constant function of $t\in\mathbb{T}$, where $\rho_{\ast}:\mathcal{A}\rightarrow \mathcal{A}/\mathcal{K}$ is the quotient map and $\mathbb{T}$ is the unit circle.