The geometric associative algebras of Euclidean space |
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Authors: | W P Joyce P H Butler |
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Institution: | 1.Department of Physics & Astronomy,University of Canterbury,Christchurch,New Zealand |
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Abstract: | We deduce two associative algebra structures arising from the homogeneity and isotropy of three dimensional space with an Euclidean geometry. These are the Clifford algebrasCl(3,0) andCl(0,3). We define a bivector as the geometric product of two vectors, a definition that differs from the usual. There is a choice of whether the bivectors are constructed tail to tail or head to head leading respectively to a positive definite or negative definite Euclidean metric. The origin of the two metric choices is not identified in the usual approach. Thus we arrive at a definite geometric answer to the question of Crumeyrolle, “What is a Bivector?”. |
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