本文選題：量子群 + 分類　； 參考：《華東師范大學(xué)》2017年碩士論文

【摘要】：本文把《Quantum Divided Power Algebra,q-Derivatives,and Some New Quantum Groups》中的三類單參數(shù)量子群Dq、(?)q、(?)q統(tǒng)一寫成雙參數(shù)量子群Dq,r(n)的商代數(shù)進(jìn)而得到Dq(?)(?)q.利用Dq,r(n)商掉適當(dāng)?shù)睦硐氡憧梢缘玫接邢蘧S點(diǎn)Hopf代數(shù)Dq,r(n,1).接著,我們重點(diǎn)考察Dq,r(n,1)模代數(shù)、半單性、擬三角結(jié)構(gòu)、同構(gòu)類個(gè)數(shù).首先,我們得到了DQ,r(n)模代數(shù)(?)Qq(n),并由dq,r(n)模代數(shù)(?)q(n)的性質(zhì)得到了Dq,r(n)與Dq,r(n,1)均為非半單的.其次,我們論證了Dq,r(n,1)具有自對(duì)偶性、Dq,r(n,1)上不存在余擬三角結(jié)構(gòu),從而得到Dq,r(n,1)上不存在擬三角結(jié)構(gòu).最后,我們給出了Dq,r(n,1)間同構(gòu)的準(zhǔn)則,利用該同構(gòu)準(zhǔn)則我們得到了:當(dāng)p為素?cái)?shù)時(shí)Dq,r(p,1)隨著參數(shù)q,r變化的同構(gòu)類個(gè)數(shù)有(P-1)2/2個(gè).
[Abstract]:In this paper, the quotient algebra of three classes of single-parameter quantum groups in < Quantum Divided Power Algebraq-Derivativesn and Some New Quantum Groups > is uniformly written into a two-parameter quantum group Dqnn.The finite dimensional point Hopf algebra DQ Hopf algebra can be obtained by using the quotient of the proper ideal.Then, we focus on the study of Dqnl) module algebra, semi-simple, quasi-triangular structure, and the number of isomorphic classes.First of all, we obtain that the DQ rn) module algebras are nonsemisimple, and from the properties of dqlr / n) module algebras, we obtain that the DQ rn) and DQ rn) are all nonsemisimple. The results are as follows: (1) in this paper, we obtain that the DQN / RN) algebra is nonsemisimple, and the properties of the DQR / RN) module algebras are both nonsemisimple.Secondly, it is proved that there is no quasi-triangular structure on the self-duality of Dqln ~ (1), so that there is no quasi-trigonometric structure on DQ ~ (r ~ (1) ~ (n ~ (1)). The conclusion is that there is no quasi-triangular structure on the DQ ~ (r ~ (1)) ~ (n ~ (1)).Finally, we give the criterion of isomorphism between Dqr and n). By using the criterion, we obtain that when p is a prime number, the number of isomorphism classes varies with the change of parameter QR, and there are two isomorphism classes with the change of parameter QR.
【學(xué)位授予單位】：華東師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O152.5

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本文編號(hào)：1750397