TY - JOUR

T1 - Some new rigidity results for stable orbit equivalence

AU - Adams, Scot

PY - 1995/4

Y1 - 1995/4

N2 - Broadly speaking, we prove that an action of a group with very little commutativity cannot be stably orbit equivalent to an action of a group with enough commutativity, assuming both actions are free and finite measure preserving. For example, one group may be SL2(ℝ) and the other a group with infinite discrete center (e.g., the universal cover of SL2(ℝ)); I believe this is the first rigidity result of this type for a pair of simpleLie groups both of split rank one. Another example: one group may be any nonelementary word hyperbolic group, the other any group with infinite discrete center.

AB - Broadly speaking, we prove that an action of a group with very little commutativity cannot be stably orbit equivalent to an action of a group with enough commutativity, assuming both actions are free and finite measure preserving. For example, one group may be SL2(ℝ) and the other a group with infinite discrete center (e.g., the universal cover of SL2(ℝ)); I believe this is the first rigidity result of this type for a pair of simpleLie groups both of split rank one. Another example: one group may be any nonelementary word hyperbolic group, the other any group with infinite discrete center.

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U2 - 10.1017/S0143385700008336

DO - 10.1017/S0143385700008336

M3 - Article

AN - SCOPUS:84974380048

SN - 0143-3857

VL - 15

SP - 209

EP - 219

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 2

ER -