Derivations of the even parts into the odd parts of the odd Hamiltonian Lie superalgebras
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摘要: 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\,$\mathbb{Z}$-齐次导子. 然后应用偶部的性质, 得到了偶部到奇部的非负\,$\mathbb{Z}$-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.
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关键词:
- 除幂代数 /
- 导子 /
- 奇Hamilton超代数
Abstract: 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 $p3,$ 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.-
Key words:
- divided power algebra /
- derivation /
- odd Hamiltonian superalgebra
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