Journal of Operator Theory

Volume 57, Issue 1, Winter 2007 pp. 3-18.

Involutive equivalence bimodules and inclusions of $C^*$-algebras with Watatani index 2

Authors: Kazunori Kodaka (1) and Tamotsu Teruya (2)
Author institution: (1) Department of Mathematical Sciences, Faculty of Science, Ryukyu University, Nishihara-cho, Okinawa 903-0213, Japan
(2) Department of Mathematical Sciences, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan

Summary: Let $A$ be a unital $C^*$-algebra. We shall introduce involutive $A$-$A$-equivalence bimodules and prove that any $C^*$-algebra containing $A$ with Watatani index 2 is constructed by an involutive $A$-$A$-equivalence bimodule.

Keywords: Conditional expectations, equivalence bimodules, Goldman type theorem, unital $C^*$-algebras, Watatani index.

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