Department of Mathematics

Mathematical Physics and Operator Algebras

  •  Patrick DeBonis, Purdue University
  •  Properties of the Actions and von Neumann algebras of Thompson-Like Groups from Cloning Systems
  •  03/21/2023
  •  10:30 AM - 11:20 AM
  •  C304 Wells Hall
  •  Brent Nelson (

Cloning systems are a method for generalizing Thompson's groups, for example $V_d$, that result in a family of groups, $\mathcal{T}_d(G_*)$, whose group von Neumann algebras have been intensely studied by Bashwinger and Zarmesky in recent years. We consider the group actions of a large class of $\mathcal{T}_d(G_*)$ and show they are stable, that is, $G \sim_{OE} G \times \mathbb{Z}.$ As a corollary, we answer Bashwinger and Zaremsky question about when $\mathcal{T}_d(G_*)$ is a McDuff Group in the sense of Deprez and Vaes. As a contrasting result, we show $L(V_d)$ is a prime II$_1$ factor. This is joint work with Rolando de Santiago and Krishnendu Khan.



Department of Mathematics
Michigan State University
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