Stable finiteness does not imply linear soficity

TL;DR

This paper demonstrates that stable finiteness in finitely generated algebras does not necessarily imply linear soficity, resolving an open question from 2017.

Contribution

It proves the existence of finitely generated, stably finite algebras that are non linear sofic, showing these properties are not equivalent.

Findings

Existence of finitely generated, stably finite algebras that are non linear sofic

Addresses an open problem from 2017

Clarifies the relationship between stable finiteness and linear soficity

Abstract

We prove that there exist finitely generated, stably finite algebras which are non linear sofic. This was left open by Arzhantseva and P\u{a}unescu in 2017.