Geodesic
On the conjugacy of measurable partitions with respect to the normalizer of a full type $\mathrm{II}_1$ ergodic group
Funkcionalʹnyj analiz i ego priloženiâ, Tome 58 (2024) no. 2, pp. 115-136 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $G$ be a countable ergodic group of automorphisms of a measure space $(X,\mu)$ and $\mathcal{N}[G]$ be the normalizer of its full group $[G]$. Problem: for a pair of measurable partitions $\xi$ and $\eta$ of the space $X$, when does there exist an element $g\in\mathcal{N}[G]$ such that $g\xi=\eta$? For a wide class of measurable partitions, we give a solution to this problem in the case where $G$ is an approximately finite group with finite invariant measure. As a consequence, we obtain results concerning the conjugacy of the commutative subalgebras that correspond to $\xi$ and $\eta$ in the type $\mathrm{II}_1$ factor constructed via the orbit partition of the group $G$.
Keywords: automorphisms of measurable space, measurable partition, full group, normalizer, von Neumann factor.
Mots-clés : orbit partitions 
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Andrei Lodkin; Benzion Rubshtein. On the conjugacy of measurable partitions with respect to the normalizer of a full type $\mathrm{II}_1$ ergodic group. Funkcionalʹnyj analiz i ego priloženiâ, Tome 58 (2024) no. 2, pp. 115-136. http://geodesic.mathdoc.fr/item/FAA_2024_58_2_a7/

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