特征3的李代数K(m,n)

Lie Algebra K(m, n)ovev Field of Characteristic 3

文献[1]证明了李代数K(m,n)(及K(m,n)的一些内蕴性质,本文证明了[1]中给出的主要性质在域F的特征数p=3时仍是正确的.

This paper proves some results of Shan Guangyu about K(m, n) are also true when the characteristic of the ground field F is equal to 3. (1) If m??0 (mod 3), then I (ad K(m, n))=m+1; If m=0(mod 3), then I(ad K(m,n))=m. (2) If m??0 (mod 3), then K(m, n) and K(m′, n′) are isomorphic if and only if m=m′, n_m=n′_mand {{n_1, n_1′},…, {n_r, n_r′}}={{n_1′, n_1′},..., {n_r′, n_r′<}}.If m??0 (mod 3),similar result is true for K(m, n)′, where m=2r+1.