PreprintCC BY 4.0arXiv
Simplicity and pure infiniteness for C*-algebras associated with stabilizers of boundary actions
Abstract
Given a discrete group Γ acting on a compact space X, and a stabilizer subgroup Λ≤ Γ of X, we use the Rieffel induction of covariant $(Λ, X)$-representations to study classes of representations induced by certain characters on Λ and the C*-algebras they generate. When X is a Γ-boundary, we obtain new classes of simple, traceless group C*-algebras. When the Γ-boundary X is an extreme boundary, we show that the associated group C*-algebras are also purely infinite, answering part of a question posed by Kalantar and Scarparo on C*-algebras associated with Thompson's groups. The latter C*-algebras are shown to be selfless in the sense of Robert.
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BibTeX
@misc{flores2026simplicity,
title = {{Simplicity and pure infiniteness for $\textC^*$-algebras associated with stabilizers of boundary actions}},
author = {Felipe Flores and Joseph Gondek},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30127},
eprint = {2608.30127},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30127},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Simplicity and pure infiniteness for C^*-algebras associated with stabilizers of boundary actions
AU - Felipe Flores
AU - Joseph Gondek
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30127
UR - https://arxiv.org/abs/2608.30127
AB - Given a discrete group Γ acting on a compact space X, and a stabilizer subgroup Λ≤ Γ of X, we use the Rieffel induction of covariant $(Λ, X)$-representations to study classes of representations induced by certain characters on Λ and the C^*-algebras they generate. When X is a Γ-boundary, we obtain new classes of simple, traceless group C^*-algebras. When the Γ-boundary X is an extreme boundary, we show that the associated group C^*-algebras are also purely infinite, answering part of a question posed by Kalantar and Scarparo on C^*-algebras associated with Thompson's groups. The latter C^*-algebras are shown to be selfless in the sense of Robert.
ER -