An Infinite Simple Group with Property (T) That Is Sofic and Hyperlinear
Brown asks in 2001 (arXiv:math/0111286, Question 11.7) whether an infinite simple discrete group with Kazhdan's property (T) can embed in the unitary group of an R^ω-embeddable McDuff factor, which for such a group is hyperlinearity; Ozawa asks it in 2003 in that language, in About the QWEP conjecture (arXiv:math/0306067); and Pestov prints it, with the sofic form added, as Open question 9.1 of Hyperlinear and sofic groups: a brief guide (arXiv:0804.3968): can an infinite simple group with Kazhdan's property (T) be hyperlinear, or sofic? This project proves, in Lean 4 over Mathlib, that the…
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