PreprintCC BY 4.0arXiv
The noncommutative topological factor theorem for rank-one product lattices
Abstract
We prove a noncommutative topological factor theorem for irreducible lattices in products of real rank-one simple Lie groups. The intermediate C*-subalgebras between the reduced group C*-algebra and the boundary crossed product are exactly the crossed products arising from coordinate subproducts of the Furstenberg boundary. This follows from a more general theorem for product boundary actions, which also yields tree and mixed local-field versions. We finally show that, for lattices in connected semisimple real Lie groups with finite center and no compact factors, the scalar-expectation case of the corresponding classification is equivalent to ordinary ITAP.
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BibTeX
@misc{houdayer2026noncommutative,
title = {{The noncommutative topological factor theorem for rank-one product lattices}},
author = {Cyril Houdayer and Corentin Le Bars},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.07421},
eprint = {2608.07421},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.07421},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The noncommutative topological factor theorem for rank-one product lattices
AU - Cyril Houdayer
AU - Corentin Le Bars
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2608.07421
UR - https://arxiv.org/abs/2608.07421
AB - We prove a noncommutative topological factor theorem for irreducible lattices in products of real rank-one simple Lie groups. The intermediate C*-subalgebras between the reduced group C*-algebra and the boundary crossed product are exactly the crossed products arising from coordinate subproducts of the Furstenberg boundary. This follows from a more general theorem for product boundary actions, which also yields tree and mixed local-field versions. We finally show that, for lattices in connected semisimple real Lie groups with finite center and no compact factors, the scalar-expectation case of the corresponding classification is equivalent to ordinary ITAP.
ER -