PreprintCC BY 4.0arXiv
Single generation of transformation group algebras
Abstract
We prove that C(X)rtimesΓ is singly generated whenever Γ is a finitely generated discrete amenable group and its action on the nonempty compact metrizable space X is free, minimal, and has the uniform Rokhlin property and Cuntz comparison of open sets. In particular, every free minimal ℤd-crossed product with metrizable underlying space is singly generated.
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BibTeX
@misc{elliott2026single,
title = {{Single generation of transformation group algebras}},
author = {George A. Elliott and Chun Guang Li and Zhuang Niu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21037},
eprint = {2610.21037},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21037},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Single generation of transformation group algebras
AU - George A. Elliott
AU - Chun Guang Li
AU - Zhuang Niu
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21037
UR - https://arxiv.org/abs/2610.21037
AB - We prove that C(X)rtimesΓ is singly generated whenever Γ is a finitely generated discrete amenable group and its action on the nonempty compact metrizable space X is free, minimal, and has the uniform Rokhlin property and Cuntz comparison of open sets. In particular, every free minimal ℤ^d-crossed product with metrizable underlying space is singly generated.
ER -