The generator problem for finite factors

Proves that every type II₁ factor with separable predual is generated by a single operator, equivalently by two self-adjoint operators, resolving the generator problem. More strongly, for every irreducible inclusion P\subset M of such factors, the unitaries u with M=W^*(P,u) form a dense G_δ subset in the trace 2-norm topology. (Lean)

Manuscript

Relative generation and the generator problem for finite factors

September 23, 2026 · source · Lean formalization available · cite as \cite{OAI:Relative-generation-and-the-generator-problem-for-finite-factors-September-23-2026}

We prove that every type II₁ factor with separable predual is generated by one operator, equivalently by two self-adjoint operators. Combined with the established direct-integral reduction to this case, this gives an affirmative solution of the generator problem for von Neumann algebras with separable predual.

Result 296 · Operator algebras. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.