4維3-李代數(shù)的實(shí)現(xiàn)和n-李代數(shù)的可解性.pdf

1、河北大學(xué)碩士學(xué)位論文4維3李代數(shù)的實(shí)現(xiàn)和n李代數(shù)的可解性姓名：劉建波申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：張知學(xué)20040501AbstractAbstractAnnLiealgebraisanaturalgeneralizationoftheconceptofaLiealgebratothecasewherethefundamentalmultiplicationoperationisnaryn≥2(Whenn=2thedefin

2、itionagreeswiththeusualdefinitionofaLiealgebra).Inthisthesiswemainlystudytherealizationof4dimensional3LiealgebrasthesolvabilityofnLiealgebras.Insection1werecallsomedefinitionsnotationsfromthetheyofnLiealgebrasgivesomebas

3、icpropertiesofnLiealgebras.SuchasdefinitionsofnLiealgebrasubalgebraidealsolvabilitysemisimplecenterquotientalgebrareduced(n1)LiealgebraClassificationTheemof(n1)dimensionalnLiealgebras.Insection2weinvestigatetherealizatio

4、nof3LiealgebrasfromafamilyofLiealgebras.WefirstlyprovetheRealizationTheemgivingthenecessaryconditionwhenafamilyofLiealgebrascanconstructa3Liealgebra.Nextweofferedaconcreteexamplerealizingalltypesof4dimensional3Liealgebra

5、s.FinallywegivesomepropertiesaboutsemisimplenLiealgebras.Insection3wemainlydiscussthesolvabilityofnLiealgebras.FirstlyweprovethreeequivalentconditionsfasolvablenLiealgebra.SubsequentlymimickingtheBelsubalgebratheyofLieal