## Séminaire d’Algèbres d’Opérateurs

### Coarse embeddings of R into II₁ factors

#### Sorin Popa - UCLA

jeudi 20 juin 2019 à 11:00
##### Salle 2015, bâtiment Sophie Germain

The hyperfinite II₁ factor R has played a central role in operator algebras ever since Murray and von Neumann introduced it in 1936-1943. It is the smallest II₁ factor, as it can be embedded in multiple ways in any other II1₁ factor M, and the unique amenable II₁ factor (Connes 1976). I have shown in 1981 that R can be embedded ergodically into any separable II₁ factor. I will discuss two new results I have obtained, along these lines :
1. Any separable II₁ factor M admits coarse embeddings of R, i.e., an embedding R↪ M such that L²M⊖L²R is a multiple of the coarse Hilbert R-bimodule L²R⊗L²Rᵒᵖ (equivalently, left-right multiplication by R on L²M⊖L²R gives a normal representation of R⊗Rᵒᵖ ).
2. Any separable II₁ factor admits an ergodic embedding of R.

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