tripartite diffie hellman with Weil pairing
This does indeed appear to be a typo. Using that $e_m$ is bilinear and alternating, one calculates
$$\begin{align*}
F_W(a,P_b,Q_c)
\;&amp;=\; e_m([b]P,[c]Q)^a
\\&amp;=\; e_m(P,Q)^{abc}
\\&amp;=\; e_m(Q,P)^{-abc}
\\&amp;=\; e_m([b]Q,[c]P)^{-a}
\\&amp;=\; F_W(a,Q_b,P_c)^{-1}
\text.
\end{align*}$$

(However, note that these are only different if the order of $e_m(P,Q))$ does not divide $abc$; in particular, we need $e_m(P,Q)\neq1$.)