lemma A.401 The invariance identity

open in the book · appendices/A-long-proofs.tex:19550 · p. 2987

Rests on

depends_on definition A.400 Invariant form, dual basis, Casimir ¶
- 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 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-240 ¶

Supports

depends_on theorem A.403 Vanishing when the Casimir is invertible ¶
- depends_on theorem A.410 Whitehead's first and second lemmas ¶
  - depends_on corollary A.411 Semisimple algebras admit no nontrivial extension ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Invariant form, dual basis, Casimir	declared	appendices/A-long-proofs.tex:19560
`depends_on`	←	Vanishing when the Casimir is invertible	declared	appendices/A-long-proofs.tex:19638
`proves`	←	app:A-long-proofs@proof-240	declared	appendices/A-long-proofs.tex:19563