Manuscript X-B-ST@1 · X-B-ST.tex · section · d03c150c

The equation ideal and separation by solutions

C3: normalization and degree-one uniqueness › The equation ideal and separation by solutions · lines 2033–2045

X-B-ST@1#eq:evaluation

For a smooth free solution define

ev_{u} ϕ (d) = ⟨ d, u ⟩ .

This is a well-defined linear evaluation on $A_{0}^{(1)}$ . The spatially compact solution evaluations separate that sector. It is not asserted to be a state on the full quantum algebra.

Displayed formulas in this passage

X-B-ST@1#eq:evaluation · line 2036
$ev_{u} ϕ (d) = ⟨ d, u ⟩ .$

Nearby in this section

lemma: Lemma: Degree-one part of the ideal
section: The equation ideal and separation by solutions
lemma: Lemma: Detection by spatially compact solutions