Contributions to the structure theory of non-simple C*-algebras

Rasmus Moritz Bentmann

Contributions to the structure theory of non-simple C*-algebras

Rasmus Moritz Bentmann

Abstract

This thesis is mainly concerned with classification results for non-simple purely ininite C*-algebras, specifically Cuntz-Krieger algebras and graph C*-algebras, and continuous fields of Kirchberg algebras. In Article A, we perform some computations concerning projective dimension in filtrated K-theory. In joint work with Sara Arklint and Takeshi Katsura, we provide a range result complementing Gunnar Restor's classification theorem for Cuntz-Kieger algebras (Article B) and we investigate reduction of filtrated K-theory for C*-algebras of real rank zero, thereby obtaining a characterization of Cuntz-Krieger algebras with primitive ideal space of accordion type (Article C). In Article D, we establish a universal coecient theorem computing Eberhard Kirchberg's ideal-related KK-groups over a finite space for algebras with vanishing boundary maps. This result is used to classify certain continuous fields of Kirchberg algebras in Article F. A stronger result for one-parameter continuous fields is obtained in joint work with Marius Dadarlat (Article E). In Article G, we compute Stefan Schwede's n-order for certain triangulated categories of C*-algebras.

Original language	English

Publisher	Department of Mathematical Sciences, Faculty of Science, University of Copenhagen
Number of pages	129
ISBN (Print)	978-87-7078-985-1
Publication status	Published - 2013

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title = "Contributions to the structure theory of non-simple C*-algebras",

abstract = "This thesis is mainly concerned with classification results for non-simple purely ininite C*-algebras, specifically Cuntz-Krieger algebras and graph C*-algebras, and continuous fields of Kirchberg algebras. In Article A, we perform some computations concerning projective dimension in filtrated K-theory. In joint work with Sara Arklint and Takeshi Katsura, we provide a range result complementing Gunnar Restor's classification theorem for Cuntz-Kieger algebras (Article B) and we investigate reduction of filtrated K-theory for C*-algebras of real rank zero, thereby obtaining a characterization of Cuntz-Krieger algebras with primitive ideal space of accordion type (Article C). In Article D, we establish a universal coecient theorem computing Eberhard Kirchberg's ideal-related KK-groups over a finite space for algebras with vanishing boundary maps. This result is used to classify certain continuous fields of Kirchberg algebras in Article F. A stronger result for one-parameter continuous fields is obtained in joint work with Marius Dadarlat (Article E). In Article G, we compute Stefan Schwede's n-order for certain triangulated categories of C*-algebras.",

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PY - 2013

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N2 - This thesis is mainly concerned with classification results for non-simple purely ininite C*-algebras, specifically Cuntz-Krieger algebras and graph C*-algebras, and continuous fields of Kirchberg algebras. In Article A, we perform some computations concerning projective dimension in filtrated K-theory. In joint work with Sara Arklint and Takeshi Katsura, we provide a range result complementing Gunnar Restor's classification theorem for Cuntz-Kieger algebras (Article B) and we investigate reduction of filtrated K-theory for C*-algebras of real rank zero, thereby obtaining a characterization of Cuntz-Krieger algebras with primitive ideal space of accordion type (Article C). In Article D, we establish a universal coecient theorem computing Eberhard Kirchberg's ideal-related KK-groups over a finite space for algebras with vanishing boundary maps. This result is used to classify certain continuous fields of Kirchberg algebras in Article F. A stronger result for one-parameter continuous fields is obtained in joint work with Marius Dadarlat (Article E). In Article G, we compute Stefan Schwede's n-order for certain triangulated categories of C*-algebras.

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M3 - Ph.D. thesis

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BT - Contributions to the structure theory of non-simple C*-algebras

PB - Department of Mathematical Sciences, Faculty of Science, University of Copenhagen

ER -

Contributions to the structure theory of non-simple C*-algebras

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