7 papers
is flexibly stable in the operator norm
Alexander Lubotzky, Guy Salomon
A cornerstone of stability theory is Voiculescu's 1983 counterexample: he constructed a sequence of pairs of unitary matrices whose commutators converge to zero in the operator nor…
Subgroups with all finite lifts isomorphic are conjugate
Ido Karshon, Alexander Lubotzky, D. B. McReynolds +2
We show that for non-conjugate subgroups and of a finite group there exists an extension of (by a finite group) in which the pre-images of and are n…
On -approximation of groups
Benjamin Bachner, Alon Dogon, Alexander Lubotzky
A longstanding open problem in the intersection of group theory and operator algebras is whether all groups are MF, that is, approximated by asymptotic representations with respect…
Conditional Non-Soficity of p-adic Deligne Extensions: on a Theorem of Gohla and Thom
Michael Chapman, Yotam Dikstein, Alexander Lubotzky
A long standing problem asks whether every group is sofic, i.e., can be separated by almost-homomorphisms to the symmetric group . Similar problems have been asked with res…
The Aldous--Lyons Conjecture I: Subgroup Tests
Lewis Bowen, Michael Chapman, Alexander Lubotzky +1
This paper, and its companion [BCV24], are devoted to a negative resolution of the Aldous--Lyons Conjecture [AL07, Ald07]. This conjecture, originated in probability theory, is wel…
Non-commutative error correcting codes and proper subgroup testing
Michael Chapman, Irit Dinur, Alexander Lubotzky
Property testing has been a major area of research in computer science in the last three decades. By property testing we refer to an ensemble of problems, results and algorithms wh…