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The Fraïssé limit of matrix algebras with the rank metric

Anderson, Aaron and Lupini, Martino (2017) The Fraïssé limit of matrix algebras with the rank metric. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20180410-092242602

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Abstract

We realize the F_q-algebra M(F_q) studied by von Neumann and Halperin as the Fraïssé limit of the class of finite-dimensional matrix algebras over a finite field F_q equipped with the rank metric. We then provide a new Fraïssé-theoretic proof of uniqueness of such an object. Using the results of Carderi and Thom, we show that the automorphism group of Aut(F_q) is extremely amenable. We deduce a Ramsey-theoretic property for the class of algebras M(F_q), and provide an explicit bound for the quantities involved.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/1712.04431arXivDiscussion Paper
ORCID:
AuthorORCID
Lupini, Martino0000-0003-1588-7057
Additional Information:A.A. was supported by Caltech’s Summer Undergraduate Research Fellowships (SURF) program and by a Rose Hills Summer Undergraduate Research Fellowship. M.L. was supported by the NSF Grant DMS-1600186.
Funders:
Funding AgencyGrant Number
Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
Rose Hills FoundationUNSPECIFIED
NSFDMS-1600186
Subject Keywords:von Neumann regular ring, rank metric, Fraïssé class, Fraïssé limit
Classification Code:2000 Mathematics Subject Classification. Primary 16E50, 03C30; Secondary 03C98
Record Number:CaltechAUTHORS:20180410-092242602
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180410-092242602
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85720
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:10 Apr 2018 18:21
Last Modified:10 Apr 2018 18:21

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