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量子群的基变换与范畴同构
引用本文:柏元淮.量子群的基变换与范畴同构[J].数学学报,1994,37(4):467-474.
作者姓名:柏元淮
作者单位:暨南大学数学系!广州510632
摘    要:令M是Z[v]的由v-1和奇素数p生成的理想,U是A=Z[v]M上相伴于对称Cartan矩阵的量子群, A-Γ是环同态, Uг=UAΓ[Uг]是Uг的量子坐标代数,本文建立了量子坐标代数的基变换:即在相关约束条件下有Г-Hopf同构 A[U]AГ≌Г[Uг].我们证明了有限秩 A自由 1型可积 U模范畴和有限秩 A自由 A[U]余模范畴是同构的.特别,当 Г是域时,局部有限 1型 Uг模范畴和Г[Uг]余模范畴是同构的.最后,我们还证明了在[1]中定义的诱导函子和B.Parshall与王建磐博士在[2]中研究的诱导函子的一致性.

关 键 词:Hopf代数  量子群  量子群的表示
收稿时间:1991-11-8
修稿时间:1992-12-4

Base Changes and Category Isomorphisms for Quantum Groups
Bai Yuanhuai.Base Changes and Category Isomorphisms for Quantum Groups[J].Acta Mathematica Sinica,1994,37(4):467-474.
Authors:Bai Yuanhuai
Institution:Bai Yuanhuai (Department of Mathematics, Jinan University, Guangzhou 510632, China)
Abstract:Let U be a quantum group over A = Zv]M with a symmetric Cartan matrix, where M is the ideal of Zv] generated by v - 1 and an odd prime p. Consider a ring homomorphism A→ Г, and let Uг = U A Г. Denote by ГUг] the quantum coordinate algebra of Uг. In this paper we show that the coordinate algebra behave, well with respect to certain base changes A→ Г. More precisely, we prove that AU] A г≌ГUг] under certain assumptions. We also give an isomorphism between the category of A-free integrable U-modules of Type 1 with finite A-rank and the category of A-free AU]-comodules with finite A-rank. Moreover, if Г is a field, we also have an isomorphism between the category of locally finite integrable Uг-modules of Type 1 and the category of ГUг]-comodules. Finally, we prove that the induction functor as defined in 1] coincides with the induction functor studied by B. Parshall and J-p. Wang in 2].
Keywords:Hopf algebra  quantum group  representation of quantum group  
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