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| COHOMOLOGY OF GRADED LIE ALGEBRASOF CARTAN TYPE $S(n,m)$ |
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Citation： |
Qiu Sen.COHOMOLOGY OF GRADED LIE ALGEBRASOF CARTAN TYPE $S(n,m)$[J].Chinese Annals of Mathematics B,1989,10(1):105~114 |
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Net amount： 755 |
Authors： |
Qiu Sen; |
Foundation： |
Supported by the Science Fund of the Chinese Academy of Sciences 842106. |
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| Abstract： |
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 $\[{H^1}(S(3,m),{\tilde V_0})\]$，where $\[{\tilde V_0}\]$ is the graded $\[S(3,m)\]$-module which is induced by an irreducible sl (3)-module $\[{V_0}\]$, the structoes 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. |
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