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Families of type III KMS states on a class of C∗-algebras containing On and QN

Journal Article


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Abstract


  • We construct a family of purely infinite C¤-algebras, Q¸ for ¸ 2 (0, 1) that are classified by their

    K-groups. There is an action of the circle T with a unique KMS state à on each Q¸. For ¸ = 1/n,

    Q1/n »= On, with its usual T action and KMS state. For ¸ = p/q, rational in lowest terms, Q¸ »= On

    (n = q − p + 1) with UHF fixed point algebra of type (pq)1. For any n > 1, Q¸ »= On for infinitely

    many ¸ with distinct KMS states and UHF fixed-point algebras. For any ¸ 2 (0, 1), Q¸ 6= O1. For

    ¸ irrational the fixed point algebras, are NOT AF and the Q¸ are usually NOT Cuntz algebras. For

    ¸ transcendental, K1(Q¸) »= K0(Q¸) »= Z1, so that Q¸ is Cuntz’ QN, [Cu1]. If ¸ and ¸−1 are both

    algebraic integers, the only On which appear are those for which n ´ 3(mod 4). For each ¸, the

    representation of Q¸ defined by the KMS state à generates a type III¸ factor. These algebras fit into

    the framework of modular index theory / twisted cyclic theory of [CPR2, CRT] and [CNNR].

Publication Date


  • 2011

Citation


  • Carey, A. L., Phillips, J., Putnam, I. F. & Rennie, A. (2011). Families of type III KMS states on a class of C∗-algebras containing On and QN. Journal of Functional Analysis, 260 (6), 1637-1681.

Scopus Eid


  • 2-s2.0-84866555502

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1742&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/736

Has Global Citation Frequency


Number Of Pages


  • 44

Start Page


  • 1637

End Page


  • 1681

Volume


  • 260

Issue


  • 6

Place Of Publication


  • United States

Abstract


  • We construct a family of purely infinite C¤-algebras, Q¸ for ¸ 2 (0, 1) that are classified by their

    K-groups. There is an action of the circle T with a unique KMS state à on each Q¸. For ¸ = 1/n,

    Q1/n »= On, with its usual T action and KMS state. For ¸ = p/q, rational in lowest terms, Q¸ »= On

    (n = q − p + 1) with UHF fixed point algebra of type (pq)1. For any n > 1, Q¸ »= On for infinitely

    many ¸ with distinct KMS states and UHF fixed-point algebras. For any ¸ 2 (0, 1), Q¸ 6= O1. For

    ¸ irrational the fixed point algebras, are NOT AF and the Q¸ are usually NOT Cuntz algebras. For

    ¸ transcendental, K1(Q¸) »= K0(Q¸) »= Z1, so that Q¸ is Cuntz’ QN, [Cu1]. If ¸ and ¸−1 are both

    algebraic integers, the only On which appear are those for which n ´ 3(mod 4). For each ¸, the

    representation of Q¸ defined by the KMS state à generates a type III¸ factor. These algebras fit into

    the framework of modular index theory / twisted cyclic theory of [CPR2, CRT] and [CNNR].

Publication Date


  • 2011

Citation


  • Carey, A. L., Phillips, J., Putnam, I. F. & Rennie, A. (2011). Families of type III KMS states on a class of C∗-algebras containing On and QN. Journal of Functional Analysis, 260 (6), 1637-1681.

Scopus Eid


  • 2-s2.0-84866555502

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1742&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/736

Has Global Citation Frequency


Number Of Pages


  • 44

Start Page


  • 1637

End Page


  • 1681

Volume


  • 260

Issue


  • 6

Place Of Publication


  • United States