The Fraïssé limit of matrix algebras with the rank metric
作者： Aaron Anderson , Martino Lupini
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摘要: We realize the F_q-algebra M(F_q) studied by von Neumann and Halperin as Fraisse limit of class finite-dimensional matrix algebras over a finite field F_q equipped with rank metric. then provide new Fraisse-theoretic proof uniqueness such an object. Using results Carderi Thom, we show that automorphism group Aut(F_q) is extremely amenable. deduce Ramsey-theoretic property for M(F_q), explicit bound quantities involved.
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harvard.edu参考文章(11)
J. L Alperin, Rowen B Bell, Groups and Representations ,(1995)
Christopher J. Eagle, Ilijas Farah, Vladyslav Kalashnyk, Bradd Hart, Martino Lupini, Boris Kadets, Fra\"iss\'e limits of C*-algebras arXiv: Logic. ,(2014) , 10.1017/JSL.2016.14
A. S. Kechris, V. G. Pestov, S. Todorcevic, Fraïssé Limits, Ramsey Theory, and topological dynamics of automorphism groups Geometric and Functional Analysis. ,vol. 15, pp. 106- 189 ,(2005) , 10.1007/S00039-005-0503-1
ITAÏ BEN YAACOV, FRAÏSSÉ LIMITS OF METRIC STRUCTURES Journal of Symbolic Logic. ,vol. 80, pp. 100- 115 ,(2015) , 10.1017/JSL.2014.71
Jure Leskovec, Deepayan Chakrabarti, Jon Kleinberg, Christos Faloutsos, Zoubin Ghahramani, None, Kronecker Graphs: An Approach to Modeling Networks Journal of Machine Learning Research. ,vol. 11, pp. 985- 1042 ,(2010)
Julien Melleray, Todor Tsankov, Extremely amenable groups via continuous logic arXiv: Logic. ,(2014)
Pierre de la Harpe, Rostislav Grigorchuk, Amenability and ergodic properties of topological groups: from Bogolyubov onwards arXiv: Group Theory. ,(2014)
Brian P. Dawkins, Israel Halperin, The isomorphism of certain continuous rings Canadian Journal of Mathematics. ,vol. 18, pp. 1333- 1344 ,(1966) , 10.4153/CJM-1966-131-4
Israel Halperin, Von Neumann's manuscript on inductive limits of regular rings Canadian Journal of Mathematics. ,vol. 20, pp. 477- 483 ,(1968) , 10.4153/CJM-1968-045-0
Martin Kassabov, Presentations of matrix rings arXiv: Rings and Algebras. ,(2009)