Jones index theory by hilbert c*-bimodules and k-theory

Tsuyoshi Kajiwara, Yasuo Watatani

    研究成果: ジャーナルへの寄稿学術誌査読

    39 被引用数 (Scopus)

    抄録

    ABSTRACT. In this paper we introduce the notion of Hubert C*-bimodules, replacing the associativity condition of two-sided inner products in Rieffel's imprimitivity bimodulcs by a Pimsner-Popa type inequality. We prove Schur's Lemma and Frobenius reciprocity in this setting. We define minimality of Hubert C*-bimodules and show that tensor products of minimal bimodules are also minimal. For an A-A bimodule which is compatible with a trace on a unital C*-algebra A, its dimension (square root of Jones index) depends only on its KK-class. Finally, we show that the dimension map transforms the Kasparov products in KK(A, A) to the product of positive real numbers, and determine the subring of KK(A, A) generated by the Hubert C*-bimodules for a C*-algebra generated by Jones projections.

    本文言語英語
    ページ(範囲)3429-3472
    ページ数44
    ジャーナルTransactions of the American Mathematical Society
    352
    8
    DOI
    出版ステータス出版済み - 2000

    !!!All Science Journal Classification (ASJC) codes

    • 数学一般
    • 応用数学

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