PreprintCC BY 4.0arXiv
Computable presentations of reduced group C*-algebras of hyperbolic groups
Abstract
Answering a question of Thomas Sinclair, we show that the standard presentation of the reduced group C*-algebra C*r(G) of an infinite hyperbolic group G is computable. The main ingredient in proving this result is showing that the Gromov boundary ∂ G of G admits a computably compact metric presentation for which the natural action of G on ∂ G is computable.
Related
- Computable presentations of reduced group C*-algebras of groups with the rapid decay property
- Non-aware computable presentations of randomizations
- Computable presentations of separable Lebesgue spaces
- Nonamenable groups whose reduced group C*-algebras are not pure
- Presentations of skein algebras of genus 2
BibTeX
@misc{goldbring2026computable,
title = {{Computable presentations of reduced group C*-algebras of hyperbolic groups}},
author = {Isaac Goldbring},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05986},
eprint = {2610.05986},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05986},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Computable presentations of reduced group C*-algebras of hyperbolic groups
AU - Isaac Goldbring
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.05986
UR - https://arxiv.org/abs/2610.05986
AB - Answering a question of Thomas Sinclair, we show that the standard presentation of the reduced group C*-algebra C^*_r(G) of an infinite hyperbolic group G is computable. The main ingredient in proving this result is showing that the Gromov boundary ∂ G of G admits a computably compact metric presentation for which the natural action of G on ∂ G is computable.
ER -