有括積的超代數及其相關問題研究.pdf

1、東北師范大學碩士學位論文有括積的超代數及其相關問題研究姓名：張爽申請學位級別：碩士專業(yè)：基礎數學指導教師：張慶成20090501AbstractInthisthesis，weconstluctanewsuperalgebralcalledsuperalgebrawithbracketcorrespondingtoLiesuperalgebra，andstudythetrivialhomologytheuniversalcentralex

2、tensionandliftingofautomorphismsandderivationsofitChapter1isdevotedtoprooftheclassicpropertiesofuniversalcenterextensionsuchas也euniquenessofuniversalcentralextension，thesufficiencyandnecessaryfortheexisitenceofuniversalc

3、entralextension，thesimplilysplitofuniversalcentralextension(ieIf石：A)BistheuniversalcentralextensionofB，thenAiSsimplilysplff，thatisAisisomorphictoitsuniversalcentralextensionie／d：A)AiSauniversalcentralextensionofA)andSOon

4、Weusereversalmethodtoshowthegeneralresult：thesufficiencyandnecessaryfortheexisitenceofuniversalcentralextensionwhichisalSOarevolutionaryinmy血esisInchapter2wediscussthecohomologytheoryofsuperalgebrawithbracket，constructth

5、etrivialhomologyofthealgebra，andobtaina5termexactsequencecorrespondingtoagivenshortexactsequencebythiswaywhichimpliesthekerneloftheuniversalcentralextensionofsuperalgebrawithbracketWeconstructauniversalcentralextensionof

6、superalgcbrawinlbracketwiⅡ1thesalnekernelobtainedinchapter2，andstudytheliftingofautomophismsandderivationsofsuperalgebrawithbracketinchapter3Keywords：universalcentralextension；liftingofautomorphism；liftingofderivations；s