R. Thompson's group $F$ and its group algebras (Logic, Algebraic system, Language and Related Areas in Computer Science)

Abstract

We have continued to study on group algebras of R. Thompson's group F. We would like to know whether these algebras satisfy the Ore condition or not. This question is directly connected to a well-known problem on F called the amenability problem. Unfortunately we have not been able to reached the answer. On the other hand, recently some research papers on this problem have been published. In this note, we first see a brief introduction for the amenability problem on Thompson's group F and then we consider Cuba's recent results ([4], [6] and [5]) on this problem. Finally, we introduce our approach and the current progress.