lemma 15.67 Multiplication is $B_{\psi}$-self-adjoint

open in the book · parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2460 · p. 628

Rests on

depends_on definition 15.66 Gram form of a functional ¶
- depends_on theorem 15.54 Completeness in the bilinear case ¶
  - depends_on definition 15.3 Tensor product Lie algebra ¶
  - depends_on lemma A.63 The invariant bilinear forms of an absolutely simple algebra form a line ¶
    - depends_on definition A.62 Absolutely simple ¶
    - proves proof app:A-long-proofs@proof-48 ¶
  - 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 ¶
  - proves proof ch:13-lie-algebra-expansions@prooflink-1 ¶
proves proof ch:13-lie-algebra-expansions@proof-36 ¶

Supports

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 ¶

Neighborhood

Every logical edge within two steps of this node.

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Edges

type	direction	node	provenance	where
`depends_on`	→	Gram form of a functional	declared	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2466
`depends_on`	←	Positive Gram forms are positive sums of real characters	declared	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2495
`proves`	←	ch:13-lie-algebra-expansions@proof-36	declared	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:2469