Journal of Operator Theory

Volume 62, Issue 2, Fall 2009 pp. 421-438.

Type II$_1$ factors with a single generator

Authors: Junhao Shen
Author institution: Department of Mathematics and Statistics, University of New Hampshire, Durham, NH, 03824, U.S.A.

Summary: In the paper, we study the generator problem for type II$_1$ factors. By defining an invariant closely related to the number of generators of a von Neumann algebra, we are able to show that a large class of type II$_1$ factors are singly generated, i.e., generated by two self-adjoint elements.

Keywords: Generator problem, type II$_1$ factor, free entropy dimension

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