The Kadison–Ringrose cohomology conjecture at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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The Kadison–Ringrose cohomology conjecture

at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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Difficulty:	🧠🧠🧠🧠🧠	Ages:	13 - ∞
Skills:	infinite matrices	Levels:	1
Category:	Operator algebras	Lean version:	YES! ✔
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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.

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LEVEL 1 Vanishing of higher bounded Hochschild cohomology

released 2026-09-23 | 4 theorems · 10 lemmas · 16 proofs · 11,514 words | PLAY LEVEL 1 » (pdf)

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.

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