Quantum lens spaces and graph algebras

Abstract

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