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

Partha Sarathi Chakraborty; S. Sundar

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

K-Theory and Homology 2010-06-10 v1 Operator Algebras

Authors: Partha Sarathi Chakraborty , S. Sundar

Abstract

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 $K_1$ .

Keywords

quantum homogeneous space K-group quantum SU(n) quantum Stiefel manifold C*-algebra unimodular element

Cite

@article{arxiv.1006.1742,
  title  = {K-groups of the quantum homogeneous space $SU_{q}(n)/SU_{q}(n-2)$},
  author = {Partha Sarathi Chakraborty and S. Sundar},
  journal= {arXiv preprint arXiv:1006.1742},
  year   = {2010}
}

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

Abstract

Keywords

Cite

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