Residual finiteness for central pushouts

2020/02/26 by Chirvasitu, Alexandru
#18A30 #20E26 #22D10 #46L09 #Category Theory (math.CT) #FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2002.11232

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∈ 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≤ G, the resulting C^*-algebra morphism is a continuous field: this is always the case for amenable G but not in general.

Related

• Central amalgamation of groups and the RFD property
• Maximal C^*-covers and residual finite-dimensionality
• RFD property for groupoid C*-algebras of amenable groupoids and for crossed products by amenable actions
• Residual finite dimensionality and representations of amenable operator algebras
• Operator spaces and residually finite-dimensional C^∗-algebras