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Stable finiteness does not imply linear soficity

Part of: Topological algebras, normed rings and algebras, Banach algebras Methods of category theory in functional analysis Homological methods

Published online by Cambridge University Press:  11 April 2023

BE’ERI GREENFELD
BE’ERI GREENFELD*
Affiliation:
Department of Mathematics, University of California, San Diego, La Jolla, CA, 92093, U.S.A. e-mail: bgreenfeld@ucsd.edu
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Abstract

We prove that there exist finitely generated, stably finite algebras which are not linear sofic. This was left open by Arzhantseva and Păunescu in 2017.

MSC classification

Primary: 46M07: Ultraproducts
Secondary: 46H99: None of the above, but in this section 16E50: von Neumann regular rings and generalizations
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 175 , Issue 2 , September 2023 , pp. 319 - 325
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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