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.