Published December 12, 2017
| Version Submitted
Discussion Paper
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The Fraïssé limit of matrix algebras with the rank metric
Creators
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.
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.Attached Files
Submitted - 1712.04431.pdf
Files
1712.04431.pdf
Additional details
Identifiers
- Eprint ID
- 85720
- Resolver ID
- CaltechAUTHORS:20180410-092242602
Related works
- Describes
- https://arxiv.org/abs/1712.04431 (URL)
Funding
- Caltech Summer Undergraduate Research Fellowship (SURF)
- Rose Hills Foundation
- NSF
- DMS-1600186
Dates
- Created
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2018-04-10Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field