可解李三超系.pdf

1、學校代碼：l絲嫂分類號t!監(jiān)研究生學號：1211604031密級：玉⑧碩士學位論文東牡I爺冠大雪可解李三超系SolvableLieTripleSupersystems作者：吳瞼蜂指導教師：陳良云剮教授學科專業(yè)：應用數(shù)學研究方向：李超代數(shù)學位類型：高師碩士東北師范大學學位評定委員會2007年5月AbstractInthisthesis，IgivesomebasicconceptionsandimportantpropertiesofLie

2、triplesupersystemsanddiscusstherelationshipsbetweenLietriplesupersystemsandLiesuperalgebrasMoreover，Igivetheclassificationof2dimensionalLietriplesupersystemsoverCandobtainsomeimportantpropertiesofLietriplesupersystemswhi

3、charebynomeanstrueforLiesuperalgebrasThemainresultsinthispaperarethefollowing：TheoremlLetTbeaLietriplesupersystemandsupposethatJisanidealofT，then【T，I，卅isanidealofTTheorem2LetTbcaLietriplesupersystem1)Supposethat^and／2are

4、solvableidealsofT，then^／2isansolvableidealsofT2)IfTbeafinite—dimensionalLietriplestlpersystelll，thenthereexistsuniquenessmaximalsolvableidealRofT，forallsolvableidealIsuchthatI∈R，Theorem3LetTbeaLietriplesupersystemandsupp

5、osethatIisanidealofT，thenthefollowingstatementshold：1)ThereexistsidealsarrayofT，I—D1122I‘2一，whicllj1=，(1)=F，，，司，，‘1=F，J2，叫口，，，j‘】2)，(‘)￡I‘，Vk∈NTheorem4LetTbeatwodimensionalLietriplcsystemoverCanddim口，ZT】=2，thenwehave1)Ti