proposition 14.50 Dimension and rank
open in the book ·
parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:1931
· p. 563
Rests on
- depends_on definition 14.20 Cartan subalgebra and rank ¶
- depends_on definition 14.49 The special unitary group in three dimensions ¶
- proves proof ch:12-lie-groups-fibre-bundles@proof-21 ¶
Supports
- depends_on lemma A.378 Real ideals and complex ideals ¶
-
depends_on
proposition 14.54
The two Casimir operators of $\mathfrak{su}(3)$
¶
- depends_on example A.358 Rank two: $\mathfrak{su}(3)$ ¶
- depends_on proposition 102.28 The parameters of QCD ¶
-
depends_on
theorem A.376
$\mathfrak{su}(3)$ is simple
¶
- depends_on corollary A.377 The adjoint representation is irreducible ¶
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:1934 |
depends_on |
→ | The special unitary group in three dimensions | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:1934 |
depends_on |
← | Real ideals and complex ideals | declared | appendices/A-long-proofs.tex:18455 |
depends_on |
← | The two Casimir operators of $\mathfrak{su}(3)$ | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2182 |
depends_on |
← | The parameters of QCD | declared | parts/11-qft-standard-model/04-qcd.tex:1083 |
depends_on |
← | $\mathfrak{su}(3)$ is simple | declared | appendices/A-long-proofs.tex:18429 |
proves |
← | ch:12-lie-groups-fibre-bundles@proof-21 | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:1937 |