凸PBW型Lyndon基与G_2型限制双参数量子群
Convex PBW-type Lyndon Basis and Restricted Two-parameter Quantum Group of Type G_2
摘要：
本文从\cite{HS}中定义的二参数量子群U_{r,s}（G_2）出发，构造了有限维点Hopf代数\mathfrak u_{r,s}（G_2）（即限制二参数量子群），证明了它是Drinfel'd双的.在给出量子根向量之间可能的对易关系后，通过确定它们的左积分和右积分，证明了在一定条件下限制量子群是带状霍普夫代数.除此之外，我们还根据左（右）斜本原元的集合的描述，确定了u_{r,s}（G_2）的所有Hopf代数同构.
英文摘要：
We construct finite-dimensional pointed Hopf algebras \mathfrak u_{r,s}(G_2) (i.e. restricted 2-parameter quantum groups) from the 2-parameter quantum group U_{r,s}(G_2) defined in \cite{HS}, which turn out to be of Drinfel'd doubles, where a crucial point is to give a detailed combinatorial construction of the convex PBW-type Lyndon basis for type G_2 in 2-parameter quantum version. After furnishing possible commutation relations among quantum root vectors, we show that the restricted quantum groups are ribbon Hopf algebras under certain conditions through determining their left and right integrals. Besides these, we determine all of the Hopf algebra isomorphisms of u_{r,s}(G_2) in terms of the description of the sets of its left (right) skew-primitive elements.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
