Singly Generated II_1 Factors

Details Singly Generated II_1 Factors Singly Generated II_1 Factors

2005-11-13

arxiv.org/abs/math/0511327v3

Mathematics

Operator Algebras

Scientific paper

In the paper, we study the generator problem of II$_1$ 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 II$_1$ factors are singly generated, i.e., generated by two self-adjoint elements. In particular, this shows that most of II$_1$ factors, whose free entropy dimensions are less than or equal to one, are singly generated.

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