奇Hamilton李超代数偶部到奇部的导子

针对特征大于3域上有限维奇Hamilton型李超代数偶部到奇部的导子问题,首先利用偶部的生成元集,通过计算导子在其生成元集上的作用,确定了偶部到奇部的负Z-齐次导子.然后应用偶部的性质,得到了偶部到奇部的非负Z-齐次导子;进而奇Hamilton李超代数偶部到奇部的导子得以刻画.所得结果对于进一步研究李超代数的结构、表示和分类有重要意义.

Derivations of the even parts into the odd parts of the odd Hamiltonian Lie superalgebras

For the problem of the derivations of the even part into
the odd part of the finite-dimensional odd Hamiltonian superalgebras
over a field of characteristic $p>3,$ by using the generating set of
the even part and calculating the action of derivations on its
generating set, the nonnegative $mathbb{Z}$-homogeneous derivations
of the even part into the odd part were determined. Furthermore, by
applying the properties of the even part, the negative
$mathbb{Z}$-homogeneous derivations of the even part into the odd
part were given. Therefore, all derivations of the even part into
the odd part of the finite-dimensional odd Hamiltonian superalgebras
were characterized, which has important significance to further
study the structure, the representation and the classification of
Lie superalgebras.