K-groups of the quantum homogeneous space $SU_{q}(n)/SU_{q}(n-2)$

Details K-groups of the quantum homogeneous space $SU_{q}(n)/SU_{q}(n-2)$ K-groups of the quantum homogeneous space $SU_{q}(n)/SU_{q}(n-2)$

2010-06-09

arxiv.org/abs/1006.1742v1

Mathematics

K-Theory and Homology

Scientific paper

Quantum Steiffel manifolds were introduced by Vainerman and Podkolzin in \cite{VP}. They classified the irreducible representations of their underlying $C^*$-algebras. Here we compute the K groups of the quantum homogeneous spaces $SU_{q}(n)/SU_{q}(n-2), n\ge 3$. Specializing to the case $n=3$ we show that the fundamental unitary for quantum $SU(3)$ is nontrivial and is a unimodular element in $K_1$.

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