lemma A.63 The invariant bilinear forms of an absolutely simple algebra form a line

open in the book · appendices/A-long-proofs.tex:4149 · p. 2823

Rests on

depends_on definition A.62 Absolutely simple ¶
proves proof app:A-long-proofs@proof-48 ¶

Supports

depends_on theorem A.64 Completeness of the factorised bilinear forms ¶
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 ¶ ↺

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`	→	Absolutely simple	declared	appendices/A-long-proofs.tex:4156
`depends_on`	←	Completeness of the factorised bilinear forms	declared	appendices/A-long-proofs.tex:4215
`depends_on`	←	Completeness in the bilinear case	declared	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2083
`proves`	←	app:A-long-proofs@proof-48	declared	appendices/A-long-proofs.tex:4159