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Non-Outer Conjugate $\mathbb{Z}_{p^2}$ --Actions on Free Product Factors

Kenneth Dykema·Maria Grazia Viola
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Abstract

We show that for any prime p and for any II$_1$ factor N there exist two $mathbb{Z}_{p^2}$-- actions on the free product factor $*_{1} ^{p}N$ that have the same outer invariant but are not outer conjugate. Therefore, in the case of free product factors, the outer invariant is not a complete invariant for outer conjugacy.

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Kenneth Dykema, Maria Grazia Viola. 2004-11-27. Non-Outer Conjugate $\mathbb{Z}_{p^2}$ --Actions on Free Product Factors. https://arxiv.org/abs/math/0411535

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