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

TL;DR

This paper demonstrates that the $C^*$-algebras of certain quantum quotient spaces can be expressed as iterated torsioned quantum double suspensions of the circle algebra, showing independence from the deformation parameter.

Contribution

It establishes an explicit isomorphism between quantum quotient spaces and iterated torsioned suspensions of $C( ext{circle})$, revealing their independence from the deformation parameter $q$.

Findings

Quantum quotient spaces are isomorphic to iterated torsioned suspensions.

These spaces are independent of the deformation parameter $q$.

Provides a new perspective on the structure of quantum homogeneous spaces.

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 $q$.