Manuscript IX-C@1 · IX-C.tex · section · 03ce8e6b

Second-stage coefficient equations and associativity

Second-stage coefficient equations and associativity · lines 1009–1032

A candidate construction must supply coefficient maps

L_{j} : L \times B \to P_{Σ}, R_{j} : B \times R \to P_{Σ}

on the orders needed below, with $L_{0}, R_{0}$ pointwise multiplication.

For the selected contraction-degree prescription, no third binary contraction against a degree-two sharp factor is present. This is a declared prescription for the candidate sector, not a consequence excluding arbitrary additional contact terms. Any departure must be separately formulated.

Write

P_{L} = A W, Q_{L} = Q_{f, g}, P_{R} = W C, Q_{R} = Q^{R}_{g, f^{'}} .

Displayed formulas in this passage

unlabeled · line 1013
$L_{j} : L \times B \to P_{Σ}, R_{j} : B \times R \to P_{Σ}$
unlabeled · line 1027
$P_{L} = A W, Q_{L} = Q_{f, g}, P_{R} = W C, Q_{R} = Q^{R}_{g, f^{'}} .$

Nearby in this section

proposition: Proposition: Formal coefficient expansion
theorem: Theorem: Coefficientwise associativity criterion
section: Second-stage coefficient equations and associativity
corollary: Corollary: Conditional placement coherence
remark: Remark: Why the corollary is not a construction
section: Second-stage coefficient equations and associativity