We introduce the notation $\mathcal{Q}(1)*\cdots*\mathcal{Q}(n)*L(\mathbf F_r)$ 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.
Dykema, K., Radulescu, F. (2003). Rescalings of free products of II-factors. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 131(06), 1813-1817 [10.1090/S0002-9939-02-06749-7].
Rescalings of free products of II-factors
RADULESCU, FLORIN
2003-01-01
Abstract
We introduce the notation $\mathcal{Q}(1)*\cdots*\mathcal{Q}(n)*L(\mathbf F_r)$ 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.File in questo prodotto:
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