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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Residual finiteness for central pushouts
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by Alexandru Chirvasitu PDF
Proc. Amer. Math. Soc. 149 (2021), 2551-2559 Request permission


We prove that pushouts $A*_CB$ of residually finite-dimensional (RFD) $C^*$-algebras over central subalgebras are always residually finite-dimensional provided the fibers $A_p$ and $B_p$, $p\in \mathrm {spec}~C$ are RFD, recovering and generalizing results by Korchagin and Courtney-Shulman. This then allows us to prove that certain central pushouts of amenable groups have RFD group $C^*$-algebras. Along the way, we discuss the problem of when, given a central group embedding $H\le G$, the resulting $C^*$-algebra morphism is a continuous field: this is always the case for amenable $G$ but not in general.
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Additional Information
  • Alexandru Chirvasitu
  • Affiliation: Department of Mathematics, University of Buffalo, Buffalo, New York 14260-2900
  • MR Author ID: 868724
  • Email:
  • Received by editor(s): April 28, 2020
  • Received by editor(s) in revised form: September 7, 2020, and September 29, 2020
  • Published electronically: March 23, 2021
  • Additional Notes: This work was partially supported by NSF grants DMS-1801011 and DMS-2001128
  • Communicated by: Adrian Ioana
  • © Copyright 2021 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 2551-2559
  • MSC (2020): Primary 46L09, 20E26, 22D10, 18A30
  • DOI:
  • MathSciNet review: 4246805