Deformations of classical Lie algebras

For a classical Lie algebra $L$ of characteristic $p>2$ and different from $C_2$ it is proved that $H^2(L,L)=0$ when $p=3$. A classical Lie algebra is understood to be the Lie algebra of a simple algebraic group, or its quotient algebra by the centre, or a Lie algebra $A_l^z$ with $l+1\equiv 0(p)$ or $E_6^z$ when $p=3$.