theorem A.426 The Kac–Moody cocycle

open in the book · appendices/A-long-proofs.tex:20900 · p. 3000

Rests on

depends_on definition A.424 Loop algebra and residue ¶
- depends_on definition 14.72 Central extension ¶
- depends_on definition 14.10 Killing form ¶
  - depends_on equation 14.5 eq:lie-structconst ¶
    - step_from equation 14.4 eq:lie-gengrlie ¶
      - step_from equation 14.3 eq:lie-generators ¶
      - step_from equation 14.2 eq:lie-varincor ¶
depends_on lemma A.425 The residue of a derivative vanishes ¶
- depends_on definition A.424 Loop algebra and residue ¶ ↺
- proves proof app:A-long-proofs@proof-255 ¶
depends_on lemma 14.11 Invariance of the Killing form ¶
- depends_on definition 14.10 Killing form ¶ ↺
- proves proof ch:12-lie-groups-fibre-bundles@proof-2 ¶
proves proof app:A-long-proofs@proof-256 ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Loop algebra and residue	declared	appendices/A-long-proofs.tex:20919
`depends_on`	→	The residue of a derivative vanishes	declared	appendices/A-long-proofs.tex:20919
`depends_on`	→	Invariance of the Killing form	declared	appendices/A-long-proofs.tex:20919
`depends_on`	←	Uniqueness in degree zero	declared	appendices/A-long-proofs.tex:21039
`proves`	←	app:A-long-proofs@proof-256	declared	appendices/A-long-proofs.tex:20923