Quantum lens spaces and graph algebras

Jeong Hee Hong and Wojciech Szymański

Vol. 211 (2003), No. 2, 249–263

DOI: 10.2140/pjm.2003.211.249

Abstract

We construct the C^∗-algebra C(L_q(p;m₁,…,m_n)) of continuous functions on the quantum lens space as the fixed point algebra for a suitable action of ℤ_p on the algebra C(S_q²ⁿ⁻¹), corresponding to the quantum odd dimensional sphere. We show that C(L_q(p;m₁,…,m_n)) is isomorphic to the graph algebra C^∗. This allows us to determine the ideal structure and, at least in principle, calculate the K-groups of C(L_q(p;m₁,…,m_n)). Passing to the limit with natural imbeddings of the quantum lens spaces we construct the quantum infinite lens space, or the quantum Eilenberg-MacLane space of type (ℤ_p,1).

Milestones

Received: 13 March 2001

Revised: 4 November 2002

Published: 1 October 2003