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Published April 10, 2018 | Submitted
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The Fraïssé limit of matrix algebras with the rank metric


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.

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August 19, 2023
August 19, 2023