Quiver方法在Hopf代數(shù)和雙Frobenius代數(shù)中的應(yīng)用.pdf

1、中國(guó)科學(xué)技術(shù)大學(xué)博士學(xué)位論文Quiver方法在Hopf代數(shù)和雙Frobenius代數(shù)中的應(yīng)用姓名：王艷華申請(qǐng)學(xué)位級(jí)別：博士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：章璞20040401AbstractThe，Baiijideaofthisthesisistoapplythequivertechniqueintherep—resentationtheoryofalgebrastothestudyofHopfalgebrasandbi—Frobeniusal

2、gebrasWefirstgiveanumericaldescriptionofaFrobeniusalgebrasoverabasiccyclebeingsymmetricUsingquivertechniqueWeconstructaclassofbi—FrobeniusalgebraswhicharenotHopfalgebrasThisfillsagapinthetheoryofbi—Froebniusalgebrasintro

3、ducedbyDoiandTakeuchiWealsoestablishthefundamentaltheoremofbi—Frobeniusmodules；andclassifybiFrobeniusalgebrasoverbasiccyclesWeputbiFrobeniusalgebrasundertheframeworkofbraidedcategory’thenobtainthefundamentaltheoremofbrai

4、dedbi—noheniusmodulesandtheexistenceofbraidedbi—FrobeniussubalgebrasWeviewtwistedHopfalgebrasfrombraidedcategoryInparticular，byusingYetterDrinfeldmodulesweconstructaclassoffinite—dimensionaltwistedHopfalgebrasNotethatall

5、knoxexamplesoftwistedHopfalgebrasareinfinitedimensionalQuasi—triangularandCOquasi，triangularHopfalgebrascanaffordsolu—tionstotheYang—BaxterequationsByusingquivertechnique，weobtainasufficientandnecessaryconditionforagener