文档介绍：摘要贮甜忙MN,卜彰一c仁咖圳一。), {0:三三,]+,[主参主]lB=一B7,c=一c7,尸=,,Ⅳ=Ⅳ7,肌M=。} [q,Hz]_0, [%?^,吃]-哦, [E,E口】=也, ‰驴k, 对V%,H2∈H 对任一根口对任一根口若口+∥不是根若口+腥根关键词:李代数SO木(2n);李代数g木(m,S,C);中心;换位子代数;Killing型;Cartan 子代数;结构公式;根系 Abstract Inthispaper,we study two kinds oftypical Liealgebra which isLiealgebra SO*(2n) and Lie algebra g}(m,S,C).In the firstithas been introduced thatsome basic knowledge ofLiealgebra andthe structure ofthetwo typicaltypes we study thetypical property oftheirsform thestarting of nature and constitute ofthe two types ofLiealgebra(.,base),and we calculated separately theirdimension,center, commutator algebra,Killing type,Caftan subalgebra,structureformula,root system,and So on. In thispaper,the following theorems have been mainly proved: Theorem A:The cemer of SO木(2n)is 0,and the center ofg木(聊,S,C)is {口玎二I口∈R}. Theorem B:Both SO木(2,z)andg术(聊,S,C)are notsimple Liealgebra. Theorem C:mutator algebra ofSO木(2n)is itsown,and mutator algebra ofg木(2n,S,C)is 贮甜忙MN,卜彤一c,,~加Ⅳ,,刎=。}, and mutator algebra ofg木(2n+1,S,C)is {0:三三,]+,[量蓥妻,]lB=一曰7,c=一c,,尸=,,Ⅳ=Ⅳ’,矶M=。} Theorem D:The Cartan subalgebra ofSO木(2n)and ***(2n,S,C)is 日={diag(xl,而,?,毛,-xa,-x2,?,-x.)lx,∈R,1≤尼≤,z}, andthe Caftan subalgebraof g木(2n+1,S,C)is 日={diag(O,五,.砭,?,%,一五,一恐,?,一x.)lxk∈R,1≤七≤,z>. Theorem E:The structuralformula ofSO宰(2n)and g木(聊,S,C)is [Hl,H2】=0, [以?五,B]-噶, [&,E口]_以, ‰驴k, 加内HI,H2∈H for any root 。for any root仅 if仪+8 lS not口root ifa+p括a root Key words:Lie Algebra SO木(2n);Lie Algebra g串(m,S,C);mutator Algebra; Killing Type;Cartan Subalgebra;Structural Formula;Root System 独创性声明本人郑重声明:所提交的学位论文是本人在导师指导下独立进行研究工作所取得的成果。据我所知,除了特别加以标注和致谢的地方外,论文中不包含其他人已经发表或撰写过的研究成果。对本人的研究做出重要贡献的个人和集体,均已在文中作了明确的说明。本声明的法律结果由本人承担。学位论文作者签名: 至塑日期: 学位论文使用授权书本学位论文作者完全了解东北师范大学有关保留、使用学位论文的规定,即: 东北师范大学有权保留并向国家有关部门或机构送交学位论文的复印件和电子版,允许论文被查阅和借阅。本人授权东北师范大学可以将学位论文的全部或部分内容编入有关数据库进行检索,可以采用影印、缩印或其它复制手段保存、汇编本学位论文。(保密的学位论文在解密后适用本授权书) 学位论文作者签名:至望日期:鱼Z:兰学位论文作者毕业后去向: 工作单位: 通讯地址: 指导教师签名: 日期: 电话: 邮编: 拦东北师范大学硕士学位论文己I 吉丁I 口挪威数学家李(Marius Shophus Lie,