Topological invariance of quantum homogeneous spaces of type $B$ and $D$

In this article, we study two families of quantum homogeneous spaces, namely, $S O_{q} (2 n + 1) / S O_{q} (2 n - 1)$ , and $S O_{q} (2 n) / S O_{q} (2 n - 2)$ . By applying a two-step Zhelobenko branching rule, we show that the $C^{*}$ -algebras $C (S O_{q} (2 n + 1) / S O_{q} (2 n - 1))$ , and $C (S O_{q} (2 n) / S O_{q} (2 n - 2))$ are generated by the entries of the first and the last rows of the fundamental matrix of the quantum groups $S O_{q} (2 n + 1)$ , and $S O_{q} (2 n)$ , 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 $S O_{q} (3)$ , $S O_{q} (5) / S O_{q} (3)$ , $S O_{q} (4) / S O_{q} (2)$ , and $S O_{q} (6) / S O_{q} (4)$ .

Topological invariance of quantum homogeneous spaces of type $B$ and $D$

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Topological invariance of quantum homogeneous spaces of type $B$ and $D$

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Topological invariance of quantum homogeneous spaces of type BB and DD

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Topological invariance of quantum homogeneous spaces of type BB and DD

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Topological invariance of quantum homogeneous spaces of type $B$ and $D$

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Topological invariance of quantum homogeneous spaces of type $B$ and $D$

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