|
Minkowski Space (number Field)
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 of a number field, 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 Footnotes References * {{cite book , first=Jürgen , last=Neukirch , authorlink=Jürgen Neukirch , title=Algebraic Number Theory , volume=322 , series=Grundlehren der Mathematischen Wissenschaften , publisher=Springer-Verlag , year=1999 , isbn=978-3-540-65399-8 , zbl=0956.11021 , mr=1697859 Algebraic number theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
