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The Weyl algebra A_n, the algebra of polynomial differential operators generated by commuting variables and their partial derivatives with the canonical commutation relations. Claims about its structure, representations, or its automorphisms and endomorphisms belong here.

The Dixmier conjecture is false for the Weyl algebra A₃.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →mathematicalA proposition of mathematics: true or false by proof rather than by observation. Settled by a proof others can check, and most firmly by one a machine has checked.constitution →Dixmier conjecture Noncommutative algebraimportance · notableImportance 0.55, from 0 to 1 · notable: a contested point in a live debate (also the default before judging). Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

Every endomorphism of the n-th Weyl algebra is an automorphism.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →definitionalA claim about what a term means. It earns a node only when the definition itself is disputed.constitution →Dixmier conjecture Noncommutative algebraimportance · notableImportance 0.60, from 0 to 1 · notable: a contested point in a live debate (also the default before judging). Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

The Dixmier conjecture is false for the Weyl algebra A_n for n ≥ 3.

SupportedThe evidence favors the claim, but the examination is incomplete or the evidence is indirect.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →importance · notableImportance 0.45, from 0 to 1 · notable: a contested point in a live debate (also the default before judging). Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

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