theorem 15.53 The factorised forms are exactly the balanced ones
open in the book ·
parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2014
· p. 623
Rests on
-
depends_on
definition 15.52
Balanced form
¶
- depends_on definition 15.3 Tensor product Lie algebra ¶
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depends_on
lemma 15.50
Every $k$-trace comes from a linear functional
¶
- depends_on definition 15.49 $k$-trace ¶
- proves proof ch:13-lie-algebra-expansions@proof-29 ¶
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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 ¶
- proves proof ch:13-lie-algebra-expansions@proof-31 ¶
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 |
→ | Balanced form | declared | parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2029 |
depends_on |
→ | Every $k$-trace comes from a linear functional | declared | parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2029 |
depends_on |
→ | Factorisation of invariant forms | declared | parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2029 |
depends_on |
← | Completeness fails for $k\ge3$ | declared | parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2103 |
proves |
← | ch:13-lie-algebra-expansions@proof-31 | declared | parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2032 |