Vol. 211, No. 2, 2003

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Quantum lens spaces and graph algebras

Jeong Hee Hong and Wojciech Szymański

Vol. 211 (2003), No. 2, 249–263
Abstract

We construct the C-algebra C(Lq(p;m1,,mn)) of continuous functions on the quantum lens space as the fixed point algebra for a suitable action of p on the algebra C(Sq2n1), corresponding to the quantum odd dimensional sphere. We show that C(Lq(p;m1,,mn)) is isomorphic to the graph algebra C(  (p;m1,...,mn))
L 2n− 1. This allows us to determine the ideal structure and, at least in principle, calculate the K-groups of C(Lq(p;m1,,mn)). 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 (p,1).

Milestones
Received: 13 March 2001
Revised: 4 November 2002
Published: 1 October 2003
Authors
Jeong Hee Hong
Applied Mathematics
Korea Maritime University
Busan 606–791
South Korea
Wojciech Szymański
Mathematics
The University of Newcastle
Callaghan, NSW 2308
Australia