Connes-Landi spheres are homogeneous spaces. (arXiv:1808.03152v1 [math.OA])

In this paper, we review some recent developments of compact quantum groups $G_\theta$ that arise as the noncommutative toric deformation of compact Lie groups $G$ of rank at least two. Noncommutative toric deformation is merely a 2-cocycle deformation using an action of a torus $\mathbb{T}^n\subset G$, $n\geq2$. Using the formula (Lemma 5.3) developed in \cite{W2018}, we construct a coaction of $SU(3)_{\theta}$ on $SU(4)_{\theta'}$ and derive that the noncommutative 7-sphere $S^7_{\theta''}$ is a homogeneous space. 查看全文>>