Rescalings of free products of II1-factors
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We introduce the notation Q(1) * . . . * Q(n) * L(Fr) for von Neumann algebra II1-factors where r is allowed to be negative. This notation is denned by rescalings of free products of II1-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.