##### Department of Mathematics,

University of California San Diego

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### Seminar in Operator Algebras

## Dan Hoff

#### UCSD

## A Class of von Neumann Algebras Which Admit Unique Prime Factorization

##### Abstract:

A tracial von Neumann algebra $M$ is called prime if it cannot be decomposed as the tensor product of two nontrivial (not type ${\rm I}$) subalgebras. Naturally, if $M$ is not prime, one asks if $M$ can be uniquely factored as a tensor product of prime subalgebras. The first result in this direction is due to Ozawa and Popa in 2003, who gave a large class of groups $\mathcal{C}$ such that for any $\Gamma_1, \dots, \Gamma_n \in \mathcal{C}$, the associated von Neumann algebra $L(\Gamma_1) \otimes \cdots \otimes L(\Gamma_n)$ is uniquely factored. This talk will focus on von Neumann algebras arising from a class of measured equivalence relations, and how the techniques of Ozawa and Popa can be adapted to this setting.

### April 24, 2015

### 2:00 PM

### AP&M 5829

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