In part two of this talk, we present a construction of type III factors arising from weighted graphs. These von Neumann algebras were originally of interest to Jones and Penneys in the context of C*-tensor categories, who conjectured that they were always free Araki–Woods factors. Using free product techniques of Dykema and Houdayer, we show this to be true. This is based on joint work with Michael Hartglass.
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