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# Mathematics > Operator Algebras

# Title: Residual finiteness for central pushouts

(Submitted on 26 Feb 2020 (v1), last revised 26 Nov 2020 (this version, v3))

Abstract: 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.

## Submission history

From: Alexandru Chirvăsitu L. [view email]**[v1]**Wed, 26 Feb 2020 00:34:55 GMT (13kb)

**[v2]**Thu, 27 Feb 2020 15:01:49 GMT (13kb)

**[v3]**Thu, 26 Nov 2020 16:02:41 GMT (14kb)

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