An induction proof of strong NF\ for amenable group C*-algebras
Abstract
We give a proof that the full group C*-algebra of a countable discrete amenable group is strong NF. The representation-theoretic construction uses the exact sequence whose kernel is the hyper-FC radical and whose quotient is the maximal ICC quotient. Extreme invariant traces on the radical induce factorial representations of the group. A Choquet decomposition of the regular radical trace selects a separating family whose induced traces are supported on the ordinary FC-centre. Exact twisted crossed-product quotients and a sequential UCT argument make their images quasidiagonal. Faithful irreducible replacements then supply the projections required for inner quasidiagonality. We also give a direct trace-decomposition variant and identify the steps shared by the two proofs.
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BibTeX
@misc{moradi2026induction,
title = {{An induction proof of strong NF\ for amenable group $C^*$-algebras}},
author = {Mehdi Moradi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00231},
eprint = {2610.00231},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00231},
}
RIS
TY - UNPB
TI - An induction proof of strong NF\ for amenable group C^*-algebras
AU - Mehdi Moradi
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00231
UR - https://arxiv.org/abs/2610.00231
AB - We give a proof that the full group C^*-algebra of a countable discrete amenable group is strong NF. The representation-theoretic construction uses the exact sequence whose kernel is the hyper-FC radical and whose quotient is the maximal ICC quotient. Extreme invariant traces on the radical induce factorial representations of the group. A Choquet decomposition of the regular radical trace selects a separating family whose induced traces are supported on the ordinary FC-centre. Exact twisted crossed-product quotients and a sequential UCT argument make their images quasidiagonal. Faithful irreducible replacements then supply the projections required for inner quasidiagonality. We also give a direct trace-decomposition variant and identify the steps shared by the two proofs.
ER -