Linear sofic groups and algebras

Arzhantseva, Goulnara; Păunescu, Liviu

doi:10.1090/tran/6706

Linear sofic groups and algebras
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by Goulnara Arzhantseva and Liviu Păunescu PDF

Trans. Amer. Math. Soc. 369 (2017), 2285-2310 Request permission

Abstract:

We introduce and systematically study linear sofic groups and linear sofic algebras. This generalizes amenable and LEF groups and algebras. We prove that a group is linear sofic if and only if its group algebra is linear sofic. We show that linear soficity for groups is a priori weaker than soficity but stronger than weak soficity. We also provide an alternative proof of a result of Elek and Szabó which states that sofic groups satisfy Kaplansky’s direct finiteness conjecture.

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