Abstract
A collection of algebras with product that preserves the metric of the underlying vector space is investigated. It is shown that this collection includes the generalized quaternions, the composition algebras, and the algebra of color. All the algebras in this collection that are either commutative or alternative are determined; the ramifications of nondegenerate metrics are detailed. If the algebra is alternative and not of dimension 1, 2, 4, or 8 over the base field, the metric must be degenerate.
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