有限维模李超代数M的限制性  

Restrictiveness of finite-dimensional modular Lie superalgebra M

作　　者：李强[1] 马丽丽[1] 韩旸[1] 

机构地区：[1]齐齐哈尔大学理学院,黑龙江齐齐哈尔161006

出　　处：《辽宁工程技术大学学报（自然科学版）》2015年第1期141-144,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：黑龙江省自然科学基金资助项目(A201210);黑龙江省教育厅科学技术研究基金资助项目(12511613)

摘　　要：为研究模李超代数M的限制性问题,把模李超代数分解成奇部成分和偶部成分.结合限制李超代数的等价定义,分别讨论了模李超代数的偶部和奇部元素的性质.利用限制李超代数的p-理想,研究了p-映射的存在性.构造p-映射,将p-映射作用在模李超代数的偶部元素上,确定存在p-半线性映射与之相关.研究结果表明:给出了模李超代数M是限制李超代数的充分必要条件,得到p-映射与p-半线性映射之间的关系.In order to solve the problem with restrictiveness of finite-dimensional modular Lie superalgebra M,this study decomposes modular Lie superalgebra M into even part and odd part. Combing the equivalent definition of restricted Lie superalgebras, the properties of elements for even part and odd part are discussed respectively. p-ideals of restricted Lie superalgebras are used to study the existence of p-mappings. Then this study constructs a p-mapping, which acts on even elements of modular Lie superalgebra M, and determines the existence of a p-semilinear mapping concerning it. The results of study give the sufficient and necessary conditions when modular Lie superalgebra M is restricted, and obtain the relation between p-mappings and p-semilinear mappings.

关 键 词：模李超代数 限制性 偶部 奇部 P-映射 p-半线性映射 

分 类 号：O152.5[理学—数学]