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The Deligne–Drinfeld conjecture

Constructing individual odd-weight elements does not establish that they freely generate the entire Lie algebra.

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Understanding the problem

Read the background

Constructing individual odd-weight elements does not establish that they freely generate the entire Lie algebra. The target includes both generation and absence of additional relations.

The coefficient field is the rationals and the completion is by weight. The claim should not be transferred to other coefficient rings or completions without an additional argument.

Why it matters

If correct, determines the full generator-and-relation structure predicted by this recognized algebraic conjecture.

What counts as progress

A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.

What to watch for

  • Assess the precise statement and assumptions before comparing results.
  • The coefficient field is the rationals and the completion is by weight. The claim should not be transferred to other coefficient rings or completions without an additional argument.
  • Track independent assessments, dependencies, corrections, and withdrawals separately from importance.

Background review: 2026-10-11. Selected sources:

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