奇Hamilton李超代数偶部到奇部的导子  

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

作　　者：华秀英[1] 刘文德[2] 

机构地区：[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

出　　处：《华东师范大学学报（自然科学版）》2014年第4期1-7,共7页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金(11171055);黑龙江省教育厅科学技术研究项目(12521114);哈尔滨理工大学青年科学研究基金(2011YF006)

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.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 Z-homogeneous derivations of the even part into the odd part were determined. Furthermore, by applying the properties of the even part, the negative 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.

关 键 词：除幂代数 导子 奇Hamilton超代数 

分 类 号：O152.5[理学—数学]