Abstract
In this paper we introduce the concept of metric Clifford algebraCℓ(V; g) for ann-dimensional real vector spaceV endowed with a metric extensor g whose signature is (p; q), withp+q=n. The metric Clifford product onCℓ (V; g) appears as a well-defined deformation (induced by g) of an euclidean Clifford product onCℓ (V). Associated with the metric extensorg; there is a gauge metric extensorh which codifies all the geometric information just contained ing: The precise form of suchh is here determined. Moreover, we present and give a proof of the so-calledgolden formula, which is important in many applications that naturally appear in our studies of multivector functions, and differential geometry and theoretical physics.
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Moya, A.M., Fernández, V.V. & Rodrigues, W.A. Metric clifford algebra. AACA 11 (Suppl 3), 49–68 (2001). https://doi.org/10.1007/BF03219147
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DOI: https://doi.org/10.1007/BF03219147