K-groups of the quantum homogeneous space SU_q(n)∕SU_q(n − 2)

Partha Sarathi Chakraborty and S. Sundar

Vol. 252 (2011), No. 2, 275–292

DOI: 10.2140/pjm.2011.252.275

Abstract

Quantum Stiefel manifolds were introduced by Vainerman and Podkolzin, who classified the irreducible representations of the C^∗-algebras underlying such manifolds. We compute the K-groups of the quantum homogeneous spaces SU_q(n)∕SU_q(n− 2) for n ≥ 3. In the case n = 3, we show that K₁ is a free ℤ-module, and the fundamental unitary for quantum SU(3) is part of a basis for K₁.

Keywords

K-groups, quantum Stiefel manifolds, quantum groups, quantum homogeneous spaces

Mathematical Subject Classification 2000

Primary: 46L80, 58B32

Milestones

Received: 23 July 2010

Accepted: 28 March 2011

Published: 29 October 2011