On Invariant Random Subgroups of Block-Diagonal Limits of Symmetric Groups

@article{Dudko2017OnIR,
  title={On Invariant Random Subgroups of Block-Diagonal Limits of Symmetric Groups},
  author={A. Dudko and Kostya Medynets},
  journal={arXiv: Group Theory},
  year={2017}
}
We classify the ergodic invariant random subgroups of block-diagonal limits of symmetric groups in the cases when the groups are simple and the associated dimension groups have finite dimensional state spaces. These block-diagonal limits arise as the transformation groups (full groups) of Bratteli diagrams that preserve the cofinality of infinite paths in the diagram. Given a simple full group $G$ admitting only a finite number of ergodic measures on the path-space $X$ of the associated… Expand
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