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| New Simple Lie Algebras of Characteristic p |
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Citation： |
Shen Guangyu.New Simple Lie Algebras of Characteristic p[J].Chinese Annals of Mathematics B,1983,4(3):329~346 |
| Page view： 828
Net amount： 751 |
Authors： |
Shen Guangyu; |
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| Abstract： |
Over an algebraically closed field F of characteristic p>3, classes of Lie algebras \Sigma= \Sigma(n, m, r, G)(m>0), \Sigma^*=\Sigma^*(n,m, r,G)(n+2\ne 0(modp))and \tilde \Sigma=\tilde \Sigma(n,m, r, G)((n+2\equiv 0(modp))are constructed, where n, m are non-negative numbers, r = (s_0+1, s_1+1, \cdots, s_n+ 1, t_1+1,\cdots,t_n+l)is a(2n+l)-tuple of positive numbers and G is a subgroup of the additive group of F. \bar \Sigma,\Sigma^* and \tidle \Sigma are shown to be all simple Lie algebras with dimensions p^N - 2, p^N and p^N — 1 respectively, where
$N=\sum\limits_i=0^n(s_i+1)+\sum\limits_i=1^n(t_i+1)+m$
Their derivation algebras are determined. It is shown that they are of generalized Cartam type K when m=0 and of generalized Cartan type H when m>0. It is then determined that \Sigma^* and \Sigma are new simple Lie algebras if n>0. Conditions of isomorphism are obtained. And a special graded algebra structure, the K-like gradation, is discussed. |
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