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Euclidean Clifford algebra

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Abstract

LetV be ann-dimensional real vector space. In this paper we introduce the concept ofeuclidean Clifford algebraCℓ (V, G E ) for a given euclidean structure onV , i.e., a pair (V, G E ) where GE is an euclidean metric forV (also called an euclidean scalar product). Our construction ofCℓ(V, G E ) has been designed to produce a powerful computational tool. We start introducing the concept ofmultivectors overV. These objects are elements of a linear space over the real field, denoted by ΛV. We introduce moreover, the concepts of exterior and euclidean scalar product of multivectors. This permits the introduction of twocontraction operators on ΛV; and the concept of euclideaninterior algebras. Equipped with these notions an euclidean Clifford product is easily introduced. We worked out with considerable details several important identities and useful formulas, to help the reader to develope a skill on the subject, preparing himself for the reading of the following papers in this series.

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Authors and Affiliations

  1. Institute of Mathematics, Statistics and Scientific Computation, IMECC-UNICAMP, CP 6065, 13083-970, Campinas, SP, Brazil

    V. V. Fernández & A. M. Moya

  2. Department of Mathematical Sciences, University of Liverpool, L69 3BX, Liverpool, UK

    W. A. Rodrigues

Authors
  1. V. V. Fernández
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  2. A. M. Moya
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  3. W. A. Rodrigues
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Fernández, V.V., Moya, A.M. & Rodrigues, W.A. Euclidean Clifford algebra. AACA 11 (Suppl 3), 1–21 (2001). https://doi.org/10.1007/BF03219144

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