量子矩阵代数Mq(2)上有限维单模的一种分类

J4 ›› 2012, Vol. 47 ›› Issue (10): 14-17.

量子矩阵代数Mq(2)上有限维单模的一种分类

王志华^1,2

1.扬州大学数学科学学院, 江苏扬州 225002;
2.南京师范大学泰州学院数学科学与应用学院，江苏泰州 225300

收稿日期:2011-11-28 出版日期:2012-11-20 发布日期:2012-10-26
作者简介:王志华(1980- )，男，讲师，博士研究生，研究方向为代数表示论. Email: mailzhihua@126.com
基金资助:
国家自然科学基金资助项目(11171291); 泰州市社会发展计划项目(2011049)

A classification of simple finite dimensional modules over quantum matrix algebra Mq(2)

WANG Zhi-hua^1,2

1. School of Mathematics, Yangzhou University, Yangzhou 225002, Jiangsu, China;
2. Department of Mathematics, Taizhou college, Nanjing Normal University, Taizhou 225300, Jiangsu, China

Received:2011-11-28 Online:2012-11-20 Published:2012-10-26

摘要/Abstract

摘要：

用初等的类似于量子群Uq(sl2)上有限维单模的分类方法, 给出了量子矩阵代数Mq(2)上有限维单模的一种分类。结果表明, 当q不是单位根时, Mq(2)上有限维单模仅有1维单模, 当q为r次单位根时(r为奇数), Mq(2)上所有单模都是有限维的, 且仅有1维与r维单模。

关键词: 量子矩阵代数; 单模; 分类

Abstract:

Using elementary methods analogue to the classification of simple finite dimensional modules of quantum group Uq(sl2), all simple finite dimensional modules of quantum matrix algebra Mq(2) are classified. It turns out that when q is not a root of unity all simple finite dimensional modules are only with dimension 1, and when q is rth root of unity with odd r all simple modules are finite with dimension 1 and r.

Key words: quantum matrix algebra; simple module; classification

王志华1,2. 量子矩阵代数Mq(2)上有限维单模的一种分类[J]. J4, 2012, 47(10): 14-17.

WANG Zhi-hua1,2. A classification of simple finite dimensional modules over quantum matrix algebra Mq(2)[J]. J4, 2012, 47(10): 14-17.

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