Cartan extensions of stabilizers of exterior forms (Q1177797)

Let \((V,\Omega)\) be a \(2n\)-dimensional symplectic vector space over complex numbers and let \(\hbox{Sp}(V)\) denote its symplectic algebra. In connection with the classification of the equations of Monge-Ampère type, the author studies the stabilizers \(\hbox{Sp}_ \omega(V)=\{g\in\hbox{Sp}(V); g\omega=0\}\) of the exterior forms \(\omega\in\Lambda(V^*)\). He deduces several conditions for \(\hbox{Sp}_ \omega(V)\) to be of infinite type.