## Jones' actions of groups of fractions

### Arnaud Brothier – 29 May 2019

Since the work of Oystein Ore in the 30's one can construct a group of fractions from a nice category. Very interesting groups arise in this way such as Richard Thompson's groups. Recently Vaughan Jones discovered that any functor starting from such a category provides an action of the associated group of fractions. In particular one can explicitly construct unitary representations or actions on various operator algebras.
I will present the general machinery of Jones and describe applications to group theory and, if time permits, to quantum field theory. Those are a joint works with Jones and Stottmeister.

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