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Subalgebras of finite codimension in semiprojective $ C^*$-algebras


Author: Dominic Enders
Journal: Proc. Amer. Math. Soc. 145 (2017), 4795-4805
MSC (2010): Primary 46L05
DOI: https://doi.org/10.1090/proc/13620
Published electronically: May 26, 2017
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Abstract: We show that semiprojectivity of a $ C^*$-algebra is preserved when passing to $ C^*$-subalgebras of finite codimension. In particular, any pullback of two semiprojective $ C^*$-algebras over a finite-dimensional $ C^*$-algebra is again semiprojective.


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Additional Information

Dominic Enders
Affiliation: Westfälische Wilhelms-Universität, Fachbereich Mathematik, Einsteinstrasse 62, 48149 Münster, Germany
Email: d.enders@uni-muenster.de

DOI: https://doi.org/10.1090/proc/13620
Received by editor(s): July 20, 2016
Received by editor(s) in revised form: December 5, 2016
Published electronically: May 26, 2017
Additional Notes: This work was supported by the SFB 878 \itshape Groups, Geometry and Actions and the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92)
Communicated by: Adrian Ioana
Article copyright: © Copyright 2017 American Mathematical Society