辫子向量代数V(R', R)

doi:10.3969/j.issn.1000-5641.2021.06.004

华东师范大学学报（自然科学版） ›› 2021, Vol. 2021 ›› Issue (6): 33-37.doi: 10.3969/j.issn.1000-5641.2021.06.004

辫子向量代数V(R', R)

胡红梅()

苏州科技大学数学科学学院, 江苏苏州　215009

收稿日期:2020-06-30 出版日期:2021-11-25 发布日期:2021-11-26
作者简介:胡红梅, 女, 副教授, 研究方向为李代数、量子群及其表示理论. E-mail: hmhu0124@126.com
基金资助:
江苏省高等学校自然科学研究项目(18KJB110027)

Braided vector algebra $ V(R',R) $

Hongmei HU()

School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou Jiangsu　 215009, China

Received:2020-06-30 Online:2021-11-25 Published:2021-11-26

摘要/Abstract

摘要：

辫子向量代数是辫子张量范畴中一类非常重要的霍普夫代数. 本文通过证明量子向量空间和辫子向量代数作为结合代数是同构的, 从而从量子包络代数 $ U_q(\mathfrak{g})$ 表示的角度详细刻画了辫子向量代数定义中的关系式, 以及定义中两个重要的 $ R$ -矩阵 $ R',R$ 满足的三个等式关系的由来.

关键词: 辫子向量代数, R-矩阵, 辫子张量范畴

Abstract:

Braided vector algebras are an important class of Hopf algebras in braided tensor categories. In this paper, it is shown that braided vector algebras are isomorphic to quantum vector spaces as associative algebras; hence, the algebraic structure of braided vector algebras and three equalities of the pair $ (R',R)$ are recovered from representations of quantized enveloping algebras $ U_q(\mathfrak g)$ .

Key words: braided vector algebras, R-matrices, braided tensor categories

中图分类号:

O154.1

胡红梅. 辫子向量代数V(R', R)[J]. 华东师范大学学报（自然科学版）, 2021, 2021(6): 33-37.

Hongmei HU. Braided vector algebra $ V(R',R) $ [J]. Journal of East China Normal University(Natural Science), 2021, 2021(6): 33-37.

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辫子向量代数V(R', R)

Braided vector algebra $ V(R',R) $

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