RESCALINGS OF FREE PRODUCTS OF II_{1}-FACTORS

KEN DYKEMA FLORIN RADULESCU

Abstract. 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.