摘要
李超代数的分类和特殊超导子代数一直是李超代数理论研究的重点。为了研究有限维李超代数超导子代数的特殊子代数性质,展开如下研究:首先,在李代数的中心导子特殊子代数理论基础上,将相关概念推广至李超代数。其次,对于非Abel幂零李超代数,利用李超代数同构理论将超导子代数相等问题转化为维数问题,给出两个特殊超导子代数相等的相关结论,再利用最小其次生成元集和Camina李超代数理论得到上述两个特殊超导子代数相等的充要条件和重要推论。最后根据李超代数同构理论和已知的特殊导子同构关系给出了其他几个特殊超导子相等的充要条件。
The classifications of Lie superalgebras and special superderivation subalgebras have always been the focus of theoretical research on Lie superalgebras.In order to study the special subalgebras properties of superderivation subalgebras in finite dimensional Lie superalgebras,the following work has been done.Firstly,based on the theory of special subalgebras of central derivations of Lie algebras,relevant concepts are extended to Lie superalgebras.Secondly,for non-Abelian nilpotent Lie superalgebras,the problem of the equality of superderivation subalgebras is transformed into a dimension problem using the isomorphism theory of Lie superalgebras,and relevant conclusions are given for the equality of two special superderivation subalgebras.Then,the necessary and sufficient conditions and important corollaries for the equality of the two special superderivation subalgebras mentioned above are obtained using the minimum secondary generator set and Camina Lie superalgebras theory.Finally,based on the isomorphism theory of Lie superalgebras and the known isomorphism relationship of special superderivations,necessary and sufficient conditions for the equality of several other special superderivations are given.
作者
尹明仁
王淑娟
刘文德
YIN Mingren;WANG Shujuan;LIU Wende(School of Mathematics and Statistics,Hainan Normal University,Haiko 571127,China;College of Science,Shanghai Maritime University,Shanghai 201306,China)
出处
《哈尔滨理工大学学报》
北大核心
2025年第3期136-140,共5页
Journal of Harbin University of Science and Technology
基金
国家自然科学基金(12061029)。
关键词
幂零李超代数
超导子
特殊超导子代数
李超代数同构
有限维李超代数
nilpotent Lie superalgebra
superderivation
special superderivation algebra
Lie superalgebra isomorphism
finite dimensional Lie superalgebra
作者简介
尹明仁(1999-),男,硕士研究生;王淑娟(1983-),女,博士,副教授,硕士研究生导师;通信作者:刘文德(1965-),男,博士,教授,博士研究生导师,E-mail:wendeliu@hrbnu.edu.cn.
