theorem 14.110 thm:lie-invpoly

open in the book · parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4490 · p. 592

Rests on

depends_on definition 14.109 $G$-invariant polynomial ¶
- depends_on equation 14.144 eq:lie-invpol-linear ¶
- depends_on equation 14.145 eq:lie-invpol-symm ¶
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 ¶
proves proof ch:12-lie-groups-fibre-bundles@proof-45 ¶

Supports

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 theorem 14.111 Chern–Weil ¶
- depends_on definition 14.115 Characteristic forms ¶
- depends_on definition 14.112 Chern–Simons form ¶
  - depends_on proposition 14.113 The Chern–Simons forms of degree $3$ and $5$ ¶
    - depends_on proposition 14.117 The quadratic invariant and its Chern–Simons form ¶
- depends_on proposition 14.114 Chern–Weil forms descend to the base ¶
  - depends_on definition 14.115 Characteristic forms ¶ ↺
- depends_on proposition 106.81 The topological charge is an integer ¶
  - depends_on proposition 106.83 The vacuum is a superposition of winding sectors ¶

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`	→	$G$-invariant polynomial	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4529
`depends_on`	→	eq:lie-structconst	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4529
`depends_on`	←	The two Casimir operators of $\mathfrak{su}(3)$	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2182
`depends_on`	←	Chern–Weil	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4708
`proves`	←	ch:12-lie-groups-fibre-bundles@proof-45	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4532