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The study of associative algebras with non-commutative multiplication — Weyl algebras, enveloping algebras, skew fields, and their ideals, modules, and endomorphisms. Claims about conjectures or results in this area belong here; commutative algebra and analysis claims do not.

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 Weyl 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 Weyl 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 →

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