OpenAlex ·
Failure of direct finiteness for group algebras in every odd characteristic
- Published
- Source
- OpenAlex
- Published in
- arXiv (Cornell University)
- DOI
- 10.48550/arxiv.2610.22536
- Original
- Read it at the publisher
- Topics
Abstract
For every odd prime $p$, we construct a finitely presented group $G_p$ and elements $a,b,c\in\mathbb{F}_p[G_p]$ such that $ab=1$, $ac=0$, and $c\ne0$. Thus $\mathbb{F}_p[G_p]$, and the group algebra over every field of characteristic $p$, fails to be directly finite. The construction combines a single exceptional self-product pair with signed bipartite cancellation. New integer matching data realize the exceptional self-intersection while retaining a strict squared-word decay estimate. We verify the adaptations needed for the earlier bounded-path and planar-localization arguments. A minimal disk picture protects the identity coefficient of $c$, so the proof does not require torsion-freeness.
The authors’ abstract, as arXiv lists it. arXiv’s listings, abstracts included, are free for anyone to reuse.
Read it on ReadSearch
Each opens after you create an account, and brings you back to this paper.
More in Mathematical Physics
Get the few papers worth your time in Mathematical Physics every morning.
ReadSearch reads the new papers in your field each day and brings you the few worth reading, each with its key finding in a sentence.