PreprintCC BY 4.0arXiv
Projections in reduced group C*-algebras with prescribed trace values in (0,1)
Abstract
Building on OpenAI's preprint, we construct, for every real number r∈(0,1), a finitely generated discrete group Gr and a projection er∈ Cr*(Gr) whose canonical trace is r. The construction encodes the geometry of expanders in the dynamics of a semidirect product of groups. For irrational r, the K-theory class [er] is not in the image of the reduced Baum--Connes map. The groups Gr have torsion and satisfy the maximal strong Novikov conjecture.
Related
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BibTeX
@misc{yu2026projections,
title = {{Projections in reduced group C*-algebras with prescribed trace values in (0,1)}},
author = {Guoliang Yu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35674},
eprint = {2610.35674},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35674},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Projections in reduced group C*-algebras with prescribed trace values in (0,1)
AU - Guoliang Yu
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35674
UR - https://arxiv.org/abs/2610.35674
AB - Building on OpenAI's preprint, we construct, for every real number r∈(0,1), a finitely generated discrete group G_r and a projection e_r∈ C_r^*(G_r) whose canonical trace is r. The construction encodes the geometry of expanders in the dynamics of a semidirect product of groups. For irrational r, the K-theory class [e_r] is not in the image of the reduced Baum--Connes map. The groups G_r have torsion and satisfy the maximal strong Novikov conjecture.
ER -