theorem 15.58 Nondegeneracy on a resonant subalgebra
open in the book ·
parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2191
· p. 624
Rests on
-
depends_on
definition 15.20
Resonant subalgebra
¶
- depends_on definition 15.18 $\Z_{2}$-grading, symmetric coset ¶
-
depends_on
definition 15.14
Truncated polynomial algebra and Takiff algebra
¶
- depends_on definition 15.3 Tensor product Lie algebra ¶
-
depends_on
lemma 15.19
A grading is an involution, and the Killing form respects it
¶
- depends_on definition 15.18 $\Z_{2}$-grading, symmetric coset ¶ ↺
- proves proof ch:13-lie-algebra-expansions@proof-10 ¶
-
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-33 ¶
Supports
- depends_on corollary 15.69 No positive pairing survives the radical ¶
- depends_on remark 15.59 The central charge is what makes the form work ¶
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 |
→ | Resonant subalgebra | declared | parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2200 |
depends_on |
→ | A grading is an involution, and the Killing form respects it | declared | parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2200 |
depends_on |
→ | Factorisation of invariant forms | declared | parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2200 |
depends_on |
← | No positive pairing survives the radical | declared | parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2579 |
depends_on |
← | The central charge is what makes the form work | declared | parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2258 |
proves |
← | ch:13-lie-algebra-expansions@proof-33 | declared | parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2203 |