Rescalings of free products of II_1-factors
Ken Dykema and Florin Radulescu
We introduce notation $Q(1) * ... * Q(n) * L(F_r)$ for von Neumann algebra II$_1$-factors where r is allowed to be negative. This notation is defined by rescalings of free products of II_1-factors, and is proved to be consistent with known results and natural operations. We also give two statements which we prove are equivalent to isomorphism of free group factors.