In mathematics, specifically the field of algebraic number theory, a Minkowski space is a Euclidean space associated with an algebraic number field.^[1]

If K is a number field of degree d then there are d distinct embeddings of K into C. We let K_C be the image of K in the product C^d, considered as equipped with the usual Hermitian inner product. If c denotes complex conjugation, let K_R denote the subspace of K_C fixed by c, equipped with a scalar product. This is the Minkowski space of K.