正特征域上一类李代数的内余分裂问题

Inner co-split problem on Lie algebras over positive characteristic field

关于李代数的余分裂和内余分裂的问题已有很多研究,但是关于正特征域上的相关结论还比较少。研究具有奇数特征p的数域上的一类李代数W(p,λ)的内余分裂问题,此类李代数中的特殊情况(λ=1)被证明是余分裂的(Xia,2012年)。通过讨论此类李代数上可能存在的余分裂结构,证明此类李代数是内余分裂李代数,当且仅当λ=1,p=3。此结果同时也给出了一类余分裂但不是内余分裂的李代数的例子。

The co-split and inner co-spih problems on ences, but there are little conclusions for the case over Lie algebras have been studied in many refer- positive characteristic field. The inner co-spilt problem on a class of Lie algebras W（p ,λ ） over field with odd characteristic p. is studied. When λ = 1, they are co-spilt. It is proved that these algebras are inner co-split algebras if and only if λ = 1 ,p = 3 by studying their possible co-split structures. This result provides a series of examples, which are not inner co-split Lie algebras but co-split.