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arXiv · 1212.6780

Linear sofic groups and algebras

Goulnara Arzhantseva·Liviu Paunescu
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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 Szabo which states that sofic groups satisfy Kaplansky's direct finiteness conjecture.

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Goulnara Arzhantseva, Liviu Paunescu. 2012-12-30. Linear sofic groups and algebras. https://arxiv.org/abs/1212.6780

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