摘要
Let F be an algebraically closed field of characteristic p】3. This paper studies the cohomology of graded Lie algebras S（n,m） of Cartan type over F. The author determines the structures of H<sup>1</sup>（S（3,m）, <sub>0</sub>）, where <sub>0</sub> is the graded S（3,m）-module which is induced by an irreducible sl （3）-module V<sub>0</sub>, the structures of H<sup>1</sup>（S（3,m）, V）, where V is an irreducible S（3,m）-module, and the structures of the restricted cohomology H<sub>*</sub><sup>1</sup>（S（3,（1, 1, 1））, V）, where V is an irreducible restricted S（3, （1, 1, 1））-module.
Let F be an algebraically closed field of characteristic p>3. This paper studies the cohomology of graded Lie algebras S(n,m) of Cartan type over F. The author determines the structures of H^1(S(3,m), _0), where _0 is the graded S(3,m)-module which is induced by an irreducible sl (3)-module V_0, the structures of H^1(S(3,m), V), where V is an irreducible S(3,m)-module, and the structures of the restricted cohomology H_*~1(S(3,(1, 1, 1)), V), where V is an irreducible restricted S(3, (1, 1, 1))-module.
基金
Supported by the Science Fund of the Chinese Academy of Sciences 842106.
