| 时空平面的Clifford代数与Abel复数系统 |
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| 引用本文： | 李武明,张雪峰.时空平面的Clifford代数与Abel复数系统[J].吉林大学学报(理学版),2007,45(5):748-752. |
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| 作者姓名： | 李武明 张雪峰 |
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| 作者单位： | 通化师范学院,数学系,吉林省,通化,134002;东北大学,理学院,沈阳,110004 |
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| 摘 要： | 证明时空平面Clifford代数Cl1,1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.
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| 关 键 词： | Clifford代数 时空代数 时空平面 Lorentz变换 Galileo变换 Euclid变换 |
| 文章编号： | 1671-5489（2007）05-0748-05 |
| 收稿时间： | 2006-12-18 |
| 修稿时间： | 2006-12-18 |
Clifford Algebra of Spacetime Plane and Abel Complex Number System |
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| LI Wu-ming,ZHANG Xue-feng.Clifford Algebra of Spacetime Plane and Abel Complex Number System[J].Journal of Jilin University: Sci Ed,2007,45(5):748-752. |
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| Authors: | LI Wu-ming ZHANG Xue-feng |
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| Institution: | 1. Department of Mathematics, Tonghua Normal University, Tonghua 134002, Jilin Province, China;2. School of Sciences, Northeastern University, Shenyang 110004, China |
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| 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 Cl1,1 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. |
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| Keywords: | Clifford algebra spacetime algebra spacetime plane Lorentz transformation Galileo transformation Euclid transformation |
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