时空平面的Clifford代数与Abel复数系统

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

Abstract

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

CLC Number:

O151.24

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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Clifford Algebra of Spacetime Plane and Abel Complex Number System

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