A Characterization of Semiprojectivity for Subhomogeneous C^*-Algebras

We study semiprojective, subhomogeneous $C^*$-algebras and give a detailed description of their structure. In particular, we find two characterizations of semiprojectivity for subhomogeneous \mbox{$C^*$-algebras}: one in terms of their primitive ideal spaces and one by means of special direct limit structures over one-dimensional NCCW complexes. These results are obtained by working out several new permanence results for semiprojectivity, including a complete description of its behavior with respect to extensions by homogeneous \mbox{$C^*$-algebras}.

2010 Mathematics Subject Classification: Primary 46L05; Secondary 46L80, 46L85, 54C55, 54F50

Keywords and Phrases: C^*-algebras, semiprojectivity, subhomogeneous, quantum permutation algebras

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