Quantum Steiffel manifolds were introduced by Vainerman and Podkolzin in [13]. They classified the irreducible representations of their underlying C * -algebras. Here we compute the K groups of the quantum homogeneous spaces SU q (n)/SU q (n − 2), n ≥ 3. Specializing to the case n = 3 we show that the fundamental unitary for quantum SU (3) is nontrivial and forms part of a generating set in the K 1 .
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