Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-25T13:51:14.162Z Has data issue: false hasContentIssue false
  • English
  • Français

Two special subgroups of the universal sofic group

Published online by Cambridge University Press:  10 April 2018

MATTEO CAVALERI ,
RADU B. MUNTEANU  and
LIVIU PĂUNESCU
MATTEO CAVALERI
Affiliation:
Institute of Mathematics of the Romanian Academy, 21 Calea Grivitei Street, 010702 Bucharest, Romania email matte.cavaleri@gmail.com, liviu.paunescu@imar.ro
RADU B. MUNTEANU
Affiliation:
Institute of Mathematics of the Romanian Academy, 21 Calea Grivitei Street, 010702 Bucharest, Romania email matte.cavaleri@gmail.com, liviu.paunescu@imar.ro Department of Mathematics, University of Bucharest, 14 Academiei Street, 010014, Bucharest, Romania email radu-bogdan.munteanu@g.unibuc.ro
LIVIU PĂUNESCU
Affiliation:
Institute of Mathematics of the Romanian Academy, 21 Calea Grivitei Street, 010702 Bucharest, Romania email matte.cavaleri@gmail.com, liviu.paunescu@imar.ro
Get access Rights & Permissions [Opens in a new window]

Abstract

We define a subgroup of the universal sofic group, obtained as the normalizer of a separable abelian subalgebra. This subgroup can be obtained as an extension by the group of automorphisms on a standard probability space. We show that each sofic representation can be conjugated inside this subgroup.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 12 , December 2019 , pp. 3250 - 3261
Copyright
© Cambridge University Press, 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arzhantseva, G. and Păunescu, L.. Almost commuting permutations are near commuting permutations. J. Funct. Anal. 269(3) (2015), 745–757.Google Scholar
Capraro, V. and Lupini, M.. Introduction to Sofic and Hyperlinear Groups and Connes’ Embedding Conjecture (Lecture Notes in Mathematics, 2136) . Springer International, Switzerland, 2015.Google Scholar
Ceccherini-Silberstein, T. and Coornaert, M.. Cellular Automata and Groups (Springer Monographs in Mathematics) . Springer, Berlin, 2010.Google Scholar
Cutland, N. J.. Nonstandard measure theory and its applications. Bull. Lond. Math. Soc. 15(6) (1983), 529–589.Google Scholar
Diaconis, P. and Graham, R. L.. Spearman’s footrule as a measure of disarray. J. Roy. Statist. Soc. Ser. B 39(2) (1977), 262–268.Google Scholar
Elek, G. and Lippner, G.. Sofic equivalence relations. J. Funct. Anal. 258(5) (2010), 1692–1708.Google Scholar
Elek, G. and Szegedy, B.. Limits of hypergraphs, removal and regularity lemmas. A non-standard approach. Preprint, 2007, arXiv:0705.2179.Google Scholar
Elek, G. and Szabó, E.. Hyperlinearity, essentially free actions and L 2 -invariants. The sofic property. Math. Ann. 332(2) (2005), 421–441.Google Scholar
Glebsky, L.. Approximations of groups, characterizations of sofic groups, and equations over groups. J. Algebra 477 (2017), 147–162.Google Scholar
Holt, D. F. and Rees, S.. Some closure results for 𝓒-approximable groups. Pacific J. Math. 287(2) (2017), 393–409.Google Scholar
Knuth, D. E.. The Art of Computer Programming, Vol. 3, Sorting and Searching, second edn. Addison-Wesley, Reading, MA, 1998.Google Scholar
Loeb, P. A.. Conversion from nonstandard to standard measure spaces and applications in probability theory. Trans. Amer. Math. Soc. 211 (1975), 113–122.Google Scholar
Ozawa, N.. Hyperlinearity, sofic groups and applications to group theory. 2009, http://people.math.jussieu.fr/∼pisier/taka.talk.pdf.Google Scholar
Păunescu, L.. On sofic actions and equivalence relations. J. Funct. Anal. 261(9) (2011), 2461–2485.Google Scholar
Pestov, V.. Hyperlinear and sofic groups: a brief guide. Bull. Symbolic Logic 14(4) (2008), 449–480.Google Scholar