The Kadison–Ringrose cohomology conjecture

Proves that every bounded Hochschild cocycle of degree at least two on a complex von Neumann algebra, with coefficients in the algebra itself, has a bounded primitive. Equivalently, all higher bounded Hochschild cohomology groups vanish, resolving the Kadison–Ringrose conjecture. (Lean)

Manuscript

Vanishing of higher bounded Hochschild cohomology

September 23, 2026 · source · cite as \cite{OAI:Vanishing-of-higher-bounded-Hochschild-cohomology-September-23-2026}

We prove that every bounded Hochschild cocycle of degree at least two on a complex von Neumann algebra, with values in the algebra itself, has a bounded primitive. Together with the established degree-one inner-derivation theorem, this resolves the Kadison–Ringrose cohomology conjecture positively.

Result 295 · 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.