华东师范大学学报（自然科学版） >

2016 , Vol. 2016 >Issue 1: 9 - 18

DOI: https://doi.org/10.3969/j.issn.1000-5641.2016.01.002

应用数学与基础数学

辫子群的q-组合式

  • 胡红梅
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  • 华东师范大学~~数学系, 上海 200241
胡红梅, 女, 博士研究生, 研究方向为量子群及其表示理论.

收稿日期: 2015-04-27

  网络出版日期: 2016-03-10

基金资助

国家自然科学基金(11271131)

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the q-commutators of braided groups

  • HU Hong-Mei
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Received date: 2015-04-27

  Online published: 2016-03-10

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摘要

从标准R-矩阵和适当选取的相互对偶的辫子群出发,作者在[1]中利用双重玻色化定理刻画了ABCD型量子包络代数U_q(mathfrakg)的递归构造.本文详细刻画在这些递归构造中,辫子群的生成元在更高一秩的新量子群中的表达式,它们是关于单根向量的q-组合式形式.

关键词：  R-矩阵; 递归构造; q-组合式; 辫子群; FRT-型生成元

本文引用格式

胡红梅 . 辫子群的q-组合式[J]. 华东师范大学学报（自然科学版）, 2016 , 2016(1) : 9 -18 . DOI: 10.3969/j.issn.1000-5641.2016.01.002

Abstract

With the standard R-matrices and suitably chosen a pair of dual braided groups, the authors gave the rank-inductive constructions of U_q}(\mathfrakg}}) for the ABCD series via the double-bosonization theory in [1]. This paper described explicitly the expressions for the generators of braided groups in the new higher rank-one quantum groups in these constructions, which are the q-commutators with the simple root vectors. These q-commutators are very important to the structure of new quantum groups.

Key words： R-matrix; rank-inductive construction; q-commutator; braided group; FRT-generator

参考文献

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