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# Journal of Operator Theory

Volume 57, Issue 2, Spring 2007  pp. 267-301.

Non-outer conjugate $\mathbb{Z}_{p^2}$-actions on free product factors

Authors Kenneth Dykema (1) and Maria Grazia Viola (2)
Author institution: (1) Department of Mathematics, Texas A\&M University, College Station TX 77843-3368, USA
(2) Department of Mathematics and Statistics, Queen's University Jeffrey Hall, University Ave., Kingston, ON Canada, K7L 3N6

Summary:  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 $*_1^pN$ that have the same outer invariant but are not outer conjugate. Therefore, the outer invariant is not a complete invariant for outer conjugacy.

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