Deformations of the Lie algebra of type \(G_2\) of characteristic 3 (Q1589184)

The authors prove that the exceptional classical Lie algebra \(L\) of type \(G_2\) over an algebraically closed field of characteristic \(p=3\) is rigid, i.e. with respect to the Zariski topology on the variety of the Lie algebra structures on the vector space of \(L\) there exists a neighborhood of \(L\) all of whose points are Lie algebras isomorphic to \(L\). This is accomplished by proving that the cohomology group \(H^2(L,L)=0\).