时空平面的Clifford代数与Abel复数系统

时空平面的Clifford代数与Abel复数系统

李武明¹, 张雪峰²

1. 通化师范学院数学系, 吉林省通化 134002; 2. 东北大学理学院, 沈阳 110004

收稿日期:2006-12-18 修回日期:1900-01-01 出版日期:2007-09-26 发布日期:2007-09-26
通讯作者: 李武明

Clifford Algebra of Spacetime Plane and Abel Complex Number System

LI Wuming¹, ZHANG Xuefeng²

1. Department of Mathematics, Tonghua Normal University, Tonghua 134002, Jilin Province, China;2. School of Sciences, Northeastern University, Shenyang 110004, China

Received:2006-12-18 Revised:1900-01-01 Online:2007-09-26 Published:2007-09-26
Contact: LI Wuming

摘要/Abstract

摘要： 证明时空平面Clifford代数Cl_1,1的3个二维子代数构成Abel复数系统的3种复数(椭圆复数、双曲复数与抛物复数), 给出了Euclid平面、 Minkowski平面及Galileo平面可在同一框架下进行研究的可行性以及Euclid变换、 Lorentz变换及Galileo变换的统一表达式.

关键词: Clifford代数, 时空代数, 时空平面, Lorentz变换, Galileo变换, Euclid变换

Abstract: It is proved that the three kinds of complex numbers (elliptic complex number, hyperbolic complex number and parabolic complex number) of Abel complex number system are composed of three 2dimensionel subalgebra of Clifford algebra Cl_1,1 in spacetime plane; and it is pointed out that the possibility of the Euclid plane, Minkowski plane and Galileo plane can be studied in the same frame. Finally the unified expression of plane Euclid transformation, Lorentz transformation and Galileo transformation is given.

Key words: Clifford algebra, spacetime algebra, spacetime plane, Lorentz transformation, Galileo transformation, Euclid transformation

中图分类号:

O151.24

李武明, 张雪峰. 时空平面的Clifford代数与Abel复数系统[J]. J4, 2007, 45(05): 748-752.

LI Wuming, ZHANG Xuefeng. Clifford Algebra of Spacetime Plane and Abel Complex Number System[J]. J4, 2007, 45(05): 748-752.

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[3]	张桂颖, 李武明, 张庆成. 实结合代数的双环与Clifford代数的结构[J]. J4, 2013, 51(03): 434-436.
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