Alphabeta Math

Kac Moody Algebras from Generalized Cartan Matrices — Examples

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How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

  • Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
  • AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
  • AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

✓ 1 result · all verified · 0 also independently AI-judged
Every result on this page is machine-checked by a proof checker and read in full and owner-audited; the judge is an additional, independent cross-model AI review of the proofs. The 1 not AI-judged were verified by owner audit (typically over a confirmed judge false positive), not failures.
1 · Prerequisites
Abstract Algebra
Lie Theory
Linear Algebra
Real Analysis
Set Theory
Topology
2 · Logical flowchart

3 · Items

Example

Rank one gcm recovers sl2

Example

The a2 serre relations

Example

The affine a1 gcm has singular rank one realization data

Example

A symmetrizable indefinite rank two gcm

Counterexample

A matrix with one zero off diagonal is not a gcm

Counterexample

Imaginary root spaces need not have multiplicity one

Sources