proposition 14.22 The rank of $\mathfrak{so}(p,q)$

open in the book · parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:665 · p. 549

Rests on

depends_on definition 14.20 Cartan subalgebra and rank ¶
depends_on equation 14.90 eq:lie-algebrasopq ¶
depends_on theorem 14.21 Racah ¶
- 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 ¶
- depends_on definition 14.20 Cartan subalgebra and rank ¶ ↺
- proves proof ch:12-lie-groups-fibre-bundles@prooflink-3 ¶
proves proof ch:12-lie-groups-fibre-bundles@proof-7 ¶

Supports

depends_on lemma 14.68 The algebra fixing a timelike momentum ¶
- depends_on definition A.384 The mass shell and the standard momentum ¶
  - depends_on lemma A.387 Standard boost and transitivity ¶
    - depends_on lemma A.388 The invariant measure ¶
      - depends_on proposition A.390 Construction ¶
    - depends_on proposition A.390 Construction ¶ ↺
  - depends_on lemma A.386 The little group ¶
    - depends_on proposition A.390 Construction ¶ ↺
  - depends_on lemma A.388 The invariant measure ¶ ↺
  - depends_on theorem A.385 Labels of a massive representation ¶
    - depends_on example A.394 $D = 4$ ¶
  - depends_on theorem A.392 Wigner–Mackey classification; quoted ¶
- depends_on lemma A.386 The little group ¶ ↺
- depends_on theorem A.385 Labels of a massive representation ¶ ↺

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`	→	Cartan subalgebra and rank	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:675
`depends_on`	→	eq:lie-algebrasopq	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:675
`depends_on`	→	Racah	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:675
`depends_on`	←	The algebra fixing a timelike momentum	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:3023
`proves`	←	ch:12-lie-groups-fibre-bundles@proof-7	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:678