李超代數(shù)的導(dǎo)子代數(shù)及單李超代數(shù).pdf

1、大連理工大學(xué)碩士學(xué)位論文李超代數(shù)的導(dǎo)子代數(shù)及單李超代數(shù)姓名：陳玉珍申請學(xué)位級別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：王穎20051216陳玉珍：李超代數(shù)的導(dǎo)子代數(shù)及單李超代數(shù)TheDerivationAlgebrasofLieSuperalgebrasandSimpleLieSuperalgebrsAbstractLiesuperalgebradealsmaiuiywiththreequestions：classification，repres

2、entationandstructureVGKacgavetheclassificationoffinitedimensionalsimpleLiesuperalgebrasoverafieldofcharacteristiczeroin1977ButthestudyofmodularLiesuperalgebrasjustbeganinrecenttenyearsTheresultsarefewUptonow，theclassific

3、ationofmodularLiesuperalgbrasisanopenproblemThispapergivessomeresultsinordertosolvetheclassificationandstructureofLiesuperalgbrasThedefinitionofaLiesuperalgebraofCaftantypewasgivenbyProfZhangYongzhengin1997Thefinitedimen

4、sionalLiesuperalgebrasofCaftantypearedividedintofourclasses：彬S，HandKThefourclassesofLiesuperalgebrasaresimpleThegeneratedsetsandderivationalgebraof日inthesituationsofchaff=p3，仇2，n1aredeterminedbyWangYLngin2004Thispapermai

5、nlygivesthederivationalgebraof日inthespecialcasesofcharF—P=3，m=2札=1ThusthederivationalgebrasofHaredeterminedcompletelyGeneralizedSimpleWeyltypealgebrasweregivenbyProfSuYucaiandZhaoKaimingin2000Theyareingeneralnongradedand

6、nonlinearTheweylalgebrasareimportantbecausesomeclassicalLiealgebrasareequivalenttothatoftheWeyltypealgebrasHowever，thestructuretheoryofgeneralizedWeyltypealgebrasdoesnotseemtobewelldevelopedLiesuperalgebrasareimportantin

7、physicsandLiesuperalgebrasdepend0nLiealgebradeeplySOweconsiderWey]typeLiesuperalgbrasnaturallyThispapergivesthedifinitionofWeylt”peLiesuperalgbrainthesamewaysandgivesanecessaryandsu伍cientconditionhereforthisLiesuperaJgeb