lemma 15.50 Every $k$-trace comes from a linear functional
open in the book ·
parts/02-mathematical-methods/13-lie-algebra-expansions.tex:1925
· p. 622
Rests on
- depends_on definition 15.49 $k$-trace ¶
- proves proof ch:13-lie-algebra-expansions@proof-29 ¶
Supports
- depends_on theorem A.64 Completeness of the factorised bilinear forms ¶
-
depends_on
theorem 15.53
The factorised forms are exactly the balanced ones
¶
- depends_on proposition 15.55 Completeness fails for $k\ge3$ ¶
-
depends_on
theorem 15.54
Completeness in the bilinear case
¶
-
depends_on
definition 15.66
Gram form of a functional
¶
- depends_on corollary 15.70 Signature of the factorised form ¶
-
depends_on
lemma 15.67
Multiplication is $B_{\psi}$-self-adjoint
¶
-
depends_on
theorem 15.68
Positive Gram forms are positive sums of real
characters
¶
- depends_on corollary 15.69 No positive pairing survives the radical ¶
-
depends_on
theorem 15.68
Positive Gram forms are positive sums of real
characters
¶
- depends_on theorem 15.68 Positive Gram forms are positive sums of real characters ¶ ↺
-
depends_on
definition 15.66
Gram form of a functional
¶
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 |
→ | $k$-trace | declared | parts/02-mathematical-methods/13-lie-algebra-expansions.tex:1934 |
depends_on |
← | Completeness of the factorised bilinear forms | declared | appendices/A-long-proofs.tex:4215 |
depends_on |
← | The factorised forms are exactly the balanced ones | declared | parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2029 |
depends_on |
← | Completeness in the bilinear case | declared | parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2083 |
proves |
← | ch:13-lie-algebra-expansions@proof-29 | declared | parts/02-mathematical-methods/13-lie-algebra-expansions.tex:1937 |