Linear sofic groups and algebras

2012/12/30 by Goulnara Arzhantseva, Arzhantseva, Goulnara, Liviu Paunescu +1
Mathematics · #03C20 #16N99 #20C07 #20E26 #20F70 #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO) #Rings and Algebras (math.RA) #math.GR #math.LO #math.RA #msc:03C20 #msc:16N99 #msc:20C07 #msc:20E26 #msc:20F70

paper · pdf · doi:10.48550/arxiv.1212.6780

34 pages

arxiv created 2012/12/30 · arxiv updated 2013/01/01

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.

Related

• Properties of Linearly Sofic Groups
• Sofic groups and direct finiteness
• On sofic groups
• Full groups and soficity
• Characterization of sofic groups and equations over groups