TY - JOUR

T1 - On the Conjugacy of Measurable Partitions with Respect to the Normalizer of a Full Type Ergodic Group

AU - Лодкин, Андрей Александрович

AU - Рубштейн, Б.А.

PY - 2024/5

Y1 - 2024/5

N2 - Let be a countable ergodic group G of automorphisms of a measure space and N be the normalizer of its full group . Problem: for a pair of measurable partitions of the space, when does there exist an element in N that comjugates these partitions. 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 the given partitions in the type II_1 factor constructed via the orbit partition of the group .

AB - Let be a countable ergodic group G of automorphisms of a measure space and N be the normalizer of its full group . Problem: for a pair of measurable partitions of the space, when does there exist an element in N that comjugates these partitions. 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 the given partitions in the type II_1 factor constructed via the orbit partition of the group .

KW - automorphisms of a measure space

KW - measurable partitions

KW - full group

KW - von Neumann factor

U2 - https://doi.org/10.1134/S0016266324020084

DO - https://doi.org/10.1134/S0016266324020084

M3 - статья

VL - 58

SP - 195

EP - 211

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

SN - 0016-2663

IS - 2

ER -