$C^*$-ALGEBRAS ASSOCIATED WITH LENS SPACES

  • Boo, Deok-Hoon (Department of Mathematics Chungnam National University) ;
  • Oh, Sei-Qwon (Department of Mathematics Chungnam National University) ;
  • Park, Chun-Gil (Department of Mathematics Chungnam National University)
  • Published : 1998.10.01

Abstract

We define the rational lens algebra (equation omitted)(n) as the crossed product by an action of Z on C( $S^{2n+l}$). Assume the fibres are $M_{ k}$/(C). We prove that (equation omitted)(n) $M_{p}$ (C) is not isomorphic to C(Prim((equation omitted)(n))) $M_{kp}$ /(C) if k > 1, and that (equation omitted)(n) $M_{p{\infty}}$ is isomorphic to C(Prim((equation omitted)(n))) $M_{k}$ /(C) $M_{p{\infty}}$ if and only if the set of prime factors of k is a subset of the set of prime factors of p. It is moreover shown that if k > 1 then (equation omitted)(n) is not stably isomorphic to C(Prim(equation omitted)(n))) $M_{k}$ (c).