## Non-tracial graph algebras, I: free Araki–Woods factors

#### Brent NelsonUniversity of California, Berkeley (UC Berkeley)Mathematics

Shlyakhtenko's free Araki–Woods factors are von Neumann algebras generated from an orthogonal representation of $\mathbb{R}$ on a real Hilbert space, and can be thought of as the type III analogue of the free group factors. They exhibit a wealth of interesting properties including, and most relevant to this talk, a resiliency under certain free products. In part one of this talk, we will recall their definition and discuss these properties as well as some methods of Dykema and Houdayer for studying free products. This is based on joint work with Michael Hartglass.

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