Singly Generated II1 Factors
Abstract
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.
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