example 15.57 $k=2$ recovers the Killing form
open in the book ·
parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2174
· p. 624
- example -- no derivation owed by its kind
Rests on
-
depends_on
theorem 15.51
Factorisation of invariant forms
¶
- depends_on definition 15.3 Tensor product Lie algebra ¶
- proves proof ch:13-lie-algebra-expansions@proof-30 ¶
-
depends_on
theorem 15.10
Factorisation of the Killing form
¶
- depends_on definition 15.3 Tensor product Lie algebra ¶ ↺
- depends_on definition 15.9 Trace form of an algebra ¶
- proves proof ch:13-lie-algebra-expansions@proof-5 ¶
Supports
- depends_on proposition 15.55 Completeness fails for $k\ge3$ ¶
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 |
→ | Factorisation of invariant forms | declared | parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2188 |
depends_on |
→ | Factorisation of the Killing form | declared | parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2188 |
depends_on |
← | Completeness fails for $k\ge3$ | declared | parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2103 |