Stable decompositions and rigidity for products of countable equivalence relations
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Stable decompositions and rigidity for products of countable equivalence relations. / Spaas, Pieter.
In: Transactions of the American Mathematical Society, Vol. 376, No. 3, 2023, p. 1867-1894.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Stable decompositions and rigidity for products of countable equivalence relations
AU - Spaas, Pieter
N1 - Publisher Copyright: © 2022 American Mathematical Society.
PY - 2023
Y1 - 2023
N2 - We show that the “stabilization” of any countable ergodic probability measure preserving (p.m.p.) equivalence relation which is not Schmidt, i.e. admits no central sequences in its full group, always gives rise to a stable equivalence relation with a unique stable decomposition, providing the first non-strongly ergodic such examples. In the proof, we moreover establish a new local characterization of the Schmidt property. We also prove some new structural results for product equivalence relations and orbit equivalence relations of diagonal product actions.
AB - We show that the “stabilization” of any countable ergodic probability measure preserving (p.m.p.) equivalence relation which is not Schmidt, i.e. admits no central sequences in its full group, always gives rise to a stable equivalence relation with a unique stable decomposition, providing the first non-strongly ergodic such examples. In the proof, we moreover establish a new local characterization of the Schmidt property. We also prove some new structural results for product equivalence relations and orbit equivalence relations of diagonal product actions.
UR - http://www.scopus.com/inward/record.url?scp=85149259480&partnerID=8YFLogxK
U2 - 10.1090/tran/8800
DO - 10.1090/tran/8800
M3 - Journal article
AN - SCOPUS:85149259480
VL - 376
SP - 1867
EP - 1894
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 3
ER -
ID: 340688926