Classification of simple graded Lie algebras with nonsemisimple component $L_0$

Two series $\mathscr R$ and $T$ of exceptional Lie algebras of characteristic 3 are constructed. It is proved that a simple 1-graded Lie algebra $L$ over an algebraically closed field of characteristic $p>2$ with component $L_0$ containing a noncentral radical is isomorphic either to one of the Lie algebras of the Cartan series $W$, $S$, and $\mathscr K$ with grading of type $(0,1)$, or to one of the Lie algebras of the series $\mathscr R$ and $T$, or to an exceptional Kostrikin–Frank Lie algebra.
Bibliography: 16 titles.