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《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (8): 65-74.doi: 10.6040/j.issn.1671-9352.0.2019.540

• • 上一篇    

B2型量子群的PBW形变及其对称性

任晓倩1,许勇军1,2*   

  1. 1. 曲阜师范大学数学科学学院, 山东 曲阜 273165;2. 山东大学数学学院, 山东 济南 250100
  • 发布日期:2020-07-14
  • 作者简介:任晓倩(1992— ), 女, 硕士研究生, 研究方向为代数学. E-mail: 2663096521@qq.com*通信作者简介: 许勇军(1984— ), 男, 博士, 副教授, 研究方向为代数学. E-mail: yjxu2002@163.com
  • 基金资助:
    国家自然科学基金资助项目(11871301);中国博士后科学基金资助项目(2016M600530);曲阜师范大学基金资助项目(BSQD20130142)

PBW-deformations of type B2 quantum group and their symmetry property

REN Xiao-qian1, XU Yong-jun1,2*   

  1. 1. School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China;
    2.School of Mathematics, Shandong University, Jinan 250100, Shandong, China
  • Published:2020-07-14

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摘要： 量子群的负部分是量子群理论中出现的一类重要的连通分次代数,其PBW形变简称为量子群的PBW形变。 除了A2情形,它们的定义关系式均是具有混合次数的齐次量子Serre关系式。 特别地, B2型量子群的负部分的定义关系式分别是次数为3和4的2个量子Serre关系式。 在连通分次代数的PBW形变理论的框架下, 本文明确刻画了B2型量子群的所有PBW形变并研究了它们的对称性, 即给出了B2型量子群的4类对合反自同构下的对称PBW形变。

关键词: 量子群, 连通分次代数, 对称PBW形变, 复杂度, 雅可比条件

Abstract: The negative parts of quantum groups are very important connected graded algebras appeared in the quantum group theory. Their PBW-deformations are called the PBW-deformations of quantum groups. Except the A2 case, the defining relations of these algebras are homogeneous quantum Serre relations with mixed degrees. In particular, the defining relations of the negative part of type B2 quantum group are respectively the homogeneous quantum Serre relations with degree 3 and 4. In this paper, in the framework of PBW-deformations of connected graded algebras, we explicitly characterize all the PBW-deformations of type B2 quantum group and investigate their symmetry property, i.e., all the symmetric PBW-deformations of type B2 quantum group under four kinds of involution anti-automorphisms are obtained.

Key words: quantum group, connected graded algebra, symmetric PBW-deformation, complexity, Jacobi conditions

中图分类号: 

  • O152.1
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