一些量子群的性质及其分类

发布时间：2018-04-14 17:40

本文选题：量子群 + 分类　；参考：《华东师范大学》2017年硕士论文

【摘要】：本文把《Quantum Divided Power Algebra,q-Derivatives,and Some New Quantum Groups》中的三类单参数量子群Dq、(?)q、(?)q统一写成双参数量子群Dq,r(n)的商代数进而得到Dq(?)(?)q.利用Dq,r(n)商掉适当的理想便可以得到有限维点Hopf代数Dq,r(n,1).接着,我们重点考察Dq,r(n,1)模代数、半单性、拟三角结构、同构类个数.首先,我们得到了DQ,r(n)模代数(?)Qq(n),并由dq,r(n)模代数(?)q(n)的性质得到了Dq,r(n)与Dq,r(n,1)均为非半单的.其次,我们论证了Dq,r(n,1)具有自对偶性、Dq,r(n,1)上不存在余拟三角结构,从而得到Dq,r(n,1)上不存在拟三角结构.最后,我们给出了Dq,r(n,1)间同构的准则,利用该同构准则我们得到了:当p为素数时Dq,r(p,1)随着参数q,r变化的同构类个数有(P-1)2/2个.
[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.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O152.5

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