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山东大学学报(理学版) ›› 2017, Vol. 52 ›› Issue (10): 12-17.doi: 10.6040/j.issn.1671-9352.0.2017.038

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量子包络代数Uq(An)的Gelfand-Kirillov维数

热比古丽·吐尼亚孜, 阿布都卡的·吾甫*   

  1. 新疆大学数学与系统科学学院, 新疆 乌鲁木齐 830046
  • 收稿日期:2017-02-10 出版日期:2017-10-20 发布日期:2017-10-12
  • 通讯作者: 阿布都卡的·吾甫(1963— ),男,博士,教授,研究方向为量子群、代数表示论及Gr(¨overo)ebner-Shirshov基理论. ;E-mail: abdu@vip.sina.com E-mail:rabigul802@sina.com
  • 作者简介:热比古丽·吐尼亚孜(1980— ),女,博士研究生,研究方向为量子群、代数表示论及Gr(¨overo)ebner-Shirshov基理论. E-mail: rabigul802@sina.com
  • 基金资助:
    国家自然科学基金资助项目(11361056)

Gelfand-Krillov dimension of quantized enveloping algebra Uq(An)

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, Xinjiang, China
  • Received:2017-02-10 Online:2017-10-20 Published:2017-10-12

摘要: 定义一个 PBW 代数Vq(An)使得量子包络代数 Uq(An)是其同态象,对 Vq(An)用Gröbner-Shirshov基方法计算量子包络代数Uq(An)的Gelfand-Kirillov维数。

关键词: Grö, PBW 代数, Gelfand-Kirillov 维数, 量子包络代数, bner-Shirshov 基

Abstract: A PBW type algebra Vq(An) is defined such that the quantized enveloping algebra Uq(An) is its homomorphic image. The Gelfand-Kirillov dimension of Uq(An)is obtained by using the Gröbner-Shirshov bases method to the algebra Vq(An).

Key words: quantized enveloping algebra, bner-Shirshov bases, Grö, PBW algebra, Gelfand-Kirillov dimension

中图分类号: 

  • O153.3
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