17114.倆類李代數(shù)的導(dǎo)子代數(shù)

1、倆類李代數(shù)的導(dǎo)子代數(shù)...................................................................................................................1摘要............................................................................................

2、.......................................................1Abstract..............................................................................................................................................2研究背景和預(yù)備知識....

3、.....................................................................................................................31.1引言.................................................................................................

4、.....................................31.2本文的主要工作...................................................................................................................4第一章qqCCDer?)(的導(dǎo)子代數(shù)......................................

5、.............................................61.1預(yù)備知識............................................................................................................................61.2導(dǎo)子代數(shù)...................................

6、...........................................................................................9第二章倆類伽利略代數(shù)的導(dǎo)子代數(shù)...............................................................................................142.1預(yù)備知識.........

7、.................................................................................................................142.2倆類伽利略代數(shù)的導(dǎo)子代數(shù)..........................................................................................

8、..15第三章結(jié)論與展望.....................................................................................................................18倆類李代數(shù)的導(dǎo)子代數(shù)摘要倆類李代數(shù)的導(dǎo)子代數(shù)摘要令ddijqq??)(是任意dd?矩陣，其中對于所有的dji??1，滿足ijq是非零復(fù)數(shù)，且jiijiiqqq???11，ijq是

9、單位根，qC為伴隨矩陣q的量子環(huán)，)(qCDer是qC的導(dǎo)子代數(shù)，本文第一部將分計算qqCCDer?)(的導(dǎo)子代數(shù)。對于21??Nl文獻(xiàn)[10]中定義了共形中心擴(kuò)張伽利略代數(shù)作為一種李代數(shù)，對于21Nl?文獻(xiàn)[10]同時也定義了無中心共形伽利略代數(shù)。本文第二部分將計算這倆類代數(shù)的導(dǎo)子代數(shù)。關(guān)鍵詞：關(guān)鍵詞：量子環(huán)導(dǎo)子代數(shù)共形中心擴(kuò)張伽利略代數(shù)中心共形伽利略代數(shù)研究背景和預(yù)備知識研究背景和預(yù)備知識1.1引言李代數(shù)起源于李群，所謂李群就是可微

10、分的群或者連續(xù)變換群。大約在1870年，李理論由挪威數(shù)學(xué)家S.Lie和德國數(shù)學(xué)家W.Killing在研究無窮小變換的概念時各自獨立發(fā)現(xiàn)的.這種數(shù)學(xué)模型在當(dāng)時人們是用“群的無限小變換”和“無窮小群”等術(shù)語來稱呼的。在1934年，德國數(shù)學(xué)家Weyl將其命名為李代數(shù)。一開始人們主要研究了有限維復(fù)半單李代數(shù)。先是德國數(shù)學(xué)家Killing（[21][22][23][24]）對復(fù)數(shù)域上的有限維單李代數(shù)進(jìn)行了初步分類。后來是法國數(shù)學(xué)家Cartan（[