Kac-Moody代數(shù)的雙極化.pdf

1、南開大學(xué)碩士研究生畢業(yè)(學(xué)位)論文姓名：年級：專業(yè)：研究方向：論文題目：導(dǎo)師：完成日期：王艷二零零三級基礎(chǔ)數(shù)學(xué)李群李代數(shù)Kac_Moody代數(shù)的雙極化孟道驥教授二零零六年五月南開大學(xué)數(shù)學(xué)科學(xué)學(xué)院數(shù)學(xué)系2006年5月AbstractAbstractInthi8thesis，somemethodsa碑百唧toc0璐tmctdipol村izationinKao—Moodyalgebrasandtheirsub柏gebras，鋤da180∞Ⅱl

2、em11stratingex鋤ple8觚eprovided7rhethesisisorganizedasfouowsSomebacl【Fo衄ds’b蠲icde缸mio珊，d愀10pments蛐dmainapplicatio地ofdip01arizationinLiealgebraswmberecalledinthe齜roductionIIlsection2，wemtrodllce8)1丑metricandnonf玎m加etricdjp0

3、1缸izationin矗nitedim伽商onalLiealgebr嬲，iethe昭mmetricdjpol甜izationinacomplexse珂扛siⅡlpleLie勤gebrawhichi8d曲erIIlinedbych觚acterelementandnonsy玎珊etricdipol齜乜ationinBordsuba玉gebraof80mereaI五踟ofac呦plex舳m磷mpleLiealgebra，whicharethe

4、basisofdip01arizationtheoryinKaDMoodyalgebras鋤dtheirsubmgel”a111ge“ion3，礬Meay砒roduce蛐fIlnd鋤ental】mowMgeofK瓣Moodyalgebr∞，whichi玎：voh電thede血mion嘰dc1姻8mcation0fgeneralizedCartanmatrices，howtoconstructKac_Moodyalgebr嬲fromthe

5、gen盯ahzedCananmatric髑柚db髂icpropert婦ofK瓣MoodyalgebI’鼬IIlgection4，we丘rstlyintroducethede血dtionof毋皿皿etrizablegenera[LizedC疵anmatric鶴，也enacl晰diⅡgtothe觚thatthere既igtsanondeg朗erate伽etricbihnearcvaluedfom0Ⅱg(A)wh池i8a880datedtoa

6、盯mmetrizablegen艘8lizedCananmatri)【，we西ve印mme七ricdipol盯ization0fg(A)wllichisdeterminedby姚er0elementZinitsCa礎(chǔ)an8ub酊gebrahsecti∞5，聊introducethede丘nition0fgeneranzedBorel8ubalgebrasandthecenterofKao—Moodyalgebr勰Accor血gtothei

7、rreLati∞8hip，we酉vethe印ec伍cmethodtoco瑚tructnons舯etricdipol舡izationinageneralizedB∞d酊balgebraIIlthe啦d，礬g№the8pe碰kreahzationofconstnlctmgnomy玎衄1etricdip01arizationingenerauzedBorelsuba培ebra0fA≯’typeKeywords：dipoIarizationKa