Dilations of C*-Correspondences and the Simplicity of Cuntz–Pimsner Algebras☆

By J. Schweizer. 2001

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The primitive ideal space of the $C^{*}$-algebras of infinite graphs (2002, unknown): “phs [28] (a class of C∗-algebras which contains both graph algebras C∗(E) and Exel-Laca algebras ØA). Related results about simplicity of Cuntz-Pimsner algebras were obtained by Schweizer in [23] and [24]. The present article is organized as follows. In §1, we review basic facts about graph algebras”
Ideal structure of C∗-algebras associated with C∗-correspondences (2003, background): “[ S ]I1/(I1∩I2) ∈ K(XI1), [S]I2/(I1∩I2) ∈ K(XI2),”
CUNTZ-PIMSNER ALGEBRAS OF GROUP ACTIONS (2004, background): “There are several general results on simplicity of the Cuntz-Pimsner algebras, which can be used to prove that the algebra OΦ is simple (see, for example [24], [22], [29]).”
GRAPH INVERSE SEMIGROUPS, GROUPOIDS AND THEIR C -ALGEBRAS (2003, unknown): “Using [18], Schweizer ([17, Corollary 5.”