I will discuss 1-bounded entropy (based on the notion of strong 1-bounded algebras due to Jung) which is a invariant of a tracial von Neumann algebra which measures “how many matricial approximations” it has. I will present discuss applications of this invariant. These include new indecomposability results for free group factors, as well as new nonisomorphism results in II1-factors, including for some crossed products by free Bogoliubov automorphisms, as well as Free-Araki woods factors.
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