theorem A.346 Racah

open in the book · appendices/A-long-proofs.tex:16906 · p. 2959

Rests on

depends_on definition 14.8 Casimir element ¶
- depends_on definition 14.5 Universal enveloping algebra ¶
  - 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 definition 14.20 Cartan subalgebra and rank ¶
depends_on theorem A.330 Cartan's criterion for semisimplicity ¶
- depends_on definition 14.10 Killing form ¶
  - depends_on equation 14.5 eq:lie-structconst ¶ ↺
- 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-209 ¶
proves proof app:A-long-proofs@proof-217 ¶

Supports

depends_on example A.359 The Lorentz algebra ¶
depends_on example A.357 Rank one: $\mathfrak{su}(2)$ ¶
depends_on example A.358 Rank two: $\mathfrak{su}(3)$ ¶

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`	→	Casimir element	declared	appendices/A-long-proofs.tex:16923
`depends_on`	→	Cartan subalgebra and rank	declared	appendices/A-long-proofs.tex:16923
`depends_on`	→	Cartan's criterion for semisimplicity	declared	appendices/A-long-proofs.tex:16923
`depends_on`	←	The Lorentz algebra	declared	appendices/A-long-proofs.tex:17297
`depends_on`	←	Rank one: $\mathfrak{su}(2)$	declared	appendices/A-long-proofs.tex:17262
`depends_on`	←	Rank two: $\mathfrak{su}(3)$	declared	appendices/A-long-proofs.tex:17278
`proves`	←	app:A-long-proofs@proof-217	declared	appendices/A-long-proofs.tex:17164