K-groups of the quantum homogeneous space $S{U}_q(n)/S{U}_q(n-2)$

Abstract

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

References in corpus (1)

• Twisted cyclic theory and an index theory for the gauge invariant KMS state on Cuntz algebras