Topological invariance of quantum homogeneous spaces of type B and D

In this article, we study two families of quantum homogeneous spaces, namely, SOq(2n+1)/SOq(2n-1), and SOq(2n)/SOq(2n-2). By applying a two-step Zhelobenko branching rule, we show that the C^*-algebras C(SOq(2n+1)/SOq(2n-1)), and C(SOq(2n)/SOq(2n-2)) are generated by the entries of the first and the last rows of the fundamental matrix of the quantum groups SOq(2n+1), and SOq(2n), respectively. We then construct a chain of short exact sequences, and using that, we compute K-groups of these spaces with explicit generators. Invoking homogeneous C^*-extension theory, we show q-independence of some intermediate C^*-algebras arising as the middle C^*-algebra of these short exact sequences. As a consequence, we get the q-invariance of SOq(5)/SOq(3) and SOq(6)/SOq(4).