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Singly Generated II_1 Factors

Junhao Shen
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Abstract

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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Junhao Shen. 2005-12-13. Singly Generated II_1 Factors. https://arxiv.org/abs/math/0511327

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