All Questions

Context: First recall some results: Actions of finite groups on the hyperfinite type $II_{1}$ factor $R$ (Jones 1980). A Galois correspondence for depth 2 irreducible subfactors (Izumi-Longo-Popa ...

The Haag-Kastler approach to quantum field theory (QFT) is one of the oldest approaches to rigorously define what a QFT is, it deals with nets of operator algebras: You start with a spacetime and ...

As you all (may) know, the Connes embedding conjecture was disproven last year. Also, as its Wikipedia page shows, there are multiple reformulations (but it is definitely not an exhaustive list): ...

The GNS construction allows one to represent a $C^*$-algebra as the algebra of bounded operators on a Hilbert space when a state is fixed, this state being represented as a vector on the Hilbert space....

A subfactor $N \subset M $ is irreducible if $N' \cap M = \mathbb{C} $. It's maximal if it admits no non-trivial intermediate subfactors $N \subset P \subset M $. It's cyclic if its lattice of ...

I'm working with von Neumann algebras and I stumbled with this statement in a work of Borchers (1999) Since $\mathcal N \subseteq \mathcal M$, it follows by standard arguments that $\Delta_{\mathcal ...