Let $\mathbb F$ be a field, $A, B, C$ vector spaces over this field and $f : A \times B \times C \to \mathbb F$ a triality. That is, $f$ is linear in its parameters and for any nonzero $b, c$ there is an $a$ such that $f(a, b, c) \neq 0$ and similar conditions hold for $b$ and $c$. Let $a_i$, $b_i$, $c_i$ be finite bases of corresponding spaces.
Question. Is there a notion analogous to that of "dual basis" - a relation on $a_i$, $b_i$, $c_i$, a sense in which it's a "good" or "correct" triplet of bases in the given spaces? Maybe there is some notion that only works when some restrictions are put on $\mathbb F$?