## Abstract

We construct a family of purely infinite C ^{*}-algebras, Qλ for λ ∈ (0, 1) that are classified by their K-groups. There is an action of the circle T with a unique KMS state ψ on each Qλ. For λ = 1/n, Q1/n≅On, with its usual T action and KMS state. For λ = p/q, rational in lowest terms, Qλ≅On (n = q - p + 1) with UHF fixed point algebra of type (p q) ^{∞}. For any n > 1, Qλ≅On for infinitely many λ with distinct KMS states and UHF fixed-point algebras. For any λ ∈ (0, 1), Qλ≠O∞. For λ irrational the fixed point algebras, are NOT AF and the Qλ are usually NOT Cuntz algebras. For λ transcendental, K1(Qλ)≅K0(Qλ)≅Z∞, so that Qλ is Cuntz' QN [Cuntz (2008) [16]]. If λ and ^{λ -1} are both algebraic integers, the only O _{n} which appear are those for which n ≡ 3 (mod 4). For each λ, the representation of Qλ defined by the KMS state ψ generates a type _{IIIλ} factor. These algebras fit into the framework of modular index theory/twisted cyclic theory of Carey et al. (2010) [8], Carey et al. (2009) [12], Carey et al. (in press) [5].

Original language | English |
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Pages (from-to) | 1637-1681 |

Number of pages | 45 |

Journal | Journal of Functional Analysis |

Volume | 260 |

Issue number | 6 |

DOIs | |

Publication status | Published - 15 Mar 2011 |

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