四元数环上的Jordan和Lie中心化子

doi:10.6040/j.issn.1671-9352.0.2021.192

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (12): 67-71.doi: 10.6040/j.issn.1671-9352.0.2021.192

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四元数环上的Jordan和Lie中心化子

曹美虹,张建华^*Symbol`@@

陕西师范大学数学与统计学院, 陕西西安 710119

发布日期:2021-11-25
作者简介:曹美虹(1996— ),女,硕士研究生,研究方向为算子代数. E-mail:meihongc@126.com*通信作者简介:张建华(1965— ),男,博士,教授,博士生导师,研究方向为算子代数. E-mail:jhzhang@snnu.edu.cn
基金资助:
国家自然科学基金资助项目(11771261)

Jordan and Lie centralizers on quaternion rings

CAO Mei-hong, ZHANG Jian-hua^*

School of Mathematics and Statistics, Shaanxi Normal University, Xian 710119, Shaanxi, China

Published:2021-11-25

摘要/Abstract

摘要： 设S是环,H(S)是S上的四元数环。通过研究H(S)上的Jordan中心化子和Lie中心化子,得到Lie中心化子是标准型的充分条件,证明在某特定假设下,H(S)上的每个Jordan中心化子是中心化子。此外,给出H(S)上的可加映射φ是中心化子的几个等价条件。

关键词: 四元数环, Jordan中心化子, Lie中心化子

Abstract: Let S be a ring, H(S) be the quaternion ring on S. By studying Jordan centralizers and Lie centralizers on H(S), this paper obtains the sufficient condition for a centralizer to be proper. Further its proved that every Jordan centralizer is a centralizer on H(S) under certain assumption. Moreover, several equivalent conditions are given that the addictive mapping φ on H(S) is centralizer.

Key words: quaternion ring, Jordan centralizer, Lie centralizer

中图分类号:

O177.1

曹美虹,张建华Symbol`@@. 四元数环上的Jordan和Lie中心化子[J]. 《山东大学学报(理学版)》, 2021, 56(12): 67-71.

CAO Mei-hong, ZHANG Jian-hua. Jordan and Lie centralizers on quaternion rings[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(12): 67-71.

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四元数环上的Jordan和Lie中心化子

Jordan and Lie centralizers on quaternion rings

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