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.[1]

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

## See also

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* Geometry of numbers

## Footnotes

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1. ^ Neukirch 1999, p. 28

## References

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* 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.