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

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 ${\ast }_1^{p}N$ 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.

32 pages, corrected typos in title and abstract