In mathematics, specifically the field of algebraic number theory, a Minkowski space is a Euclidean space associated with an algebraic number field.
If K is a number field of degree d then there are d distinct embeddings of K into C. We let K<sub>C</sub> be the image of K in the product C<sup>d</sup>, considered as equipped with the usual Hermitian inner product. If c denotes complex conjugation, let K<sub>R</sub> denote the subspace of K<sub>C</sub> fixed by c, equipped with a scalar product. This is the Minkowski space of K.