Minkowski space (number field)

For Minkowski space-time, see Minkowski space.

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_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.

See also

• Geometry of numbers

References

• Neukirch, Jürgen (1999). Algebraic Number Theory. Grundlehren der Mathematischen Wissenschaften. Vol. 322. Springer-Verlag. ISBN 978-3-540-65399-8. MR 1697859. Zbl 0956.11021.