W型限制李代数的内余分裂问题

The inner co-split question of the W type restricted Lie algebras

研究正特征域上的一类李代数W(n;1=)的内余分裂问题。李代数W(n;1=)是正特征域F上的一类单的限制型李代数,假设域特征Char F=p是奇数,在n=1,p≥5和n≥2两种情况下,分别证明李代数W(n;1=)上不可能存在内余分裂结构。由于n=1,p=3时W(n;1=)是内余分裂的,证明李代数W(n;1=)是内余分裂李代数,当且仅当n=1,p=3。

Consider the inner co-split problem of Lie algebras W（ n ; 1 ） over positive characteristic fields. The Lie algebra W（ n;1） is a restricted simple Lie algebra over positive characteristic field F. Assume that ChafF = p is odd. Under conditions n = 1, p ≥ 5 and n≥ 2 respectively, it is proved that W（ n ; 1） has no inner co-split structure. Since it is known that W（n; 1） has an inner co-split in case of n = 1, p = 3 , so it can be obtained that W（n;1 has an inner co-split if and only if n = 1, p = 3 .