Anderson, Aaron and Lupini, Martino (2017) The Fraïssé limit of matrix algebras with the rank metric. . (Submitted) https://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) | ||||||||
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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. | ||||||||
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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: | https://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: | 03 Oct 2019 19:34 |
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