2005/11/13 by Junhao Shen, Shen, Junhao
Mathematics · #FOS: Mathematics #Operator Algebras (math.OA) #math.OA
paper · pdf · doi:10.48550/arxiv.math/0511327
arxiv created 2005/12/13 · arxiv updated 2009/12/01
In the paper, we study the generator problem of II1 factors. By defining a new concept related to the number of generators of a von Neumann algebra, we are able to show that a large class of II1 factors are singly generated, i.e., generated by two self-adjoint elements. In particular, this shows that most of II1 factors, whose free entropy dimensions are less than or equal to one, are singly generated.