华东师范大学学报(自然科学版) ›› 2014, Vol. 2014 ›› Issue (4): 1-7.

• 应用数学与基础数学 •    下一篇

奇Hamilton李超代数偶部到奇部的导子

华秀英1,  刘文德2   

  1. 1. 哈尔滨理工大学~~应用科学学院,~~哈尔滨 150080;
    2. 哈尔滨师范大学~~数学科学学院, ~~哈尔滨 150025
  • 收稿日期:2013-07-01 修回日期:2013-10-01 出版日期:2014-07-25 发布日期:2014-07-25

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

HUA Xiu-ying1,  LIU Wen-de2   

  1. 1. School of Applied Sciences, Harbin University of Science and Technology, Harbin  150080, China;
    2. School of Mathematical Sciences, Harbin Normal University, Harbin 150025, China
  • Received:2013-07-01 Revised:2013-10-01 Online:2014-07-25 Published:2014-07-25

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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.

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 $p>3,$ 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.

Key words: divided power algebra, derivation, odd Hamiltonian superalgebra

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