About: Pfister form     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : yago:WikicatQuadraticForms, within Data Space : dbpedia.org associated with source document(s)
QRcode icon
http://dbpedia.org/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FPfister_form&graph=http%3A%2F%2Fdbpedia.org&graph=http%3A%2F%2Fdbpedia.org

In mathematics, a Pfister form is a particular kind of quadratic form, introduced by Albrecht Pfister in 1965. In what follows, quadratic forms are considered over a field F of characteristic not 2. For a natural number n, an n-fold Pfister form over F is a quadratic form of dimension 2n that can be written as a tensor product of quadratic forms So the 1-fold and 2-fold Pfister forms look like: . The n-fold Pfister forms additively generate the n-th power I n of the fundamental ideal of the Witt ring of F.

AttributesValues
rdf:type
rdfs:label
  • Pfister form (en)
rdfs:comment
  • In mathematics, a Pfister form is a particular kind of quadratic form, introduced by Albrecht Pfister in 1965. In what follows, quadratic forms are considered over a field F of characteristic not 2. For a natural number n, an n-fold Pfister form over F is a quadratic form of dimension 2n that can be written as a tensor product of quadratic forms So the 1-fold and 2-fold Pfister forms look like: . The n-fold Pfister forms additively generate the n-th power I n of the fundamental ideal of the Witt ring of F. (en)
dcterms:subject
Wikipage page ID
Wikipage revision ID
Link from a Wikipage to another Wikipage
sameAs
dbp:wikiPageUsesTemplate
has abstract
  • In mathematics, a Pfister form is a particular kind of quadratic form, introduced by Albrecht Pfister in 1965. In what follows, quadratic forms are considered over a field F of characteristic not 2. For a natural number n, an n-fold Pfister form over F is a quadratic form of dimension 2n that can be written as a tensor product of quadratic forms for some nonzero elements a1, ..., an of F. (Some authors omit the signs in this definition; the notation here simplifies the relation to Milnor K-theory, discussed below.) An n-fold Pfister form can also be constructed inductively from an (n−1)-fold Pfister form q and a nonzero element a of F, as . So the 1-fold and 2-fold Pfister forms look like: . For n ≤ 3, the n-fold Pfister forms are norm forms of composition algebras. In that case, two n-fold Pfister forms are isomorphic if and only if the corresponding composition algebras are isomorphic. In particular, this gives the classification of octonion algebras. The n-fold Pfister forms additively generate the n-th power I n of the fundamental ideal of the Witt ring of F. (en)
prov:wasDerivedFrom
page length (characters) of wiki page
foaf:isPrimaryTopicOf
is Link from a Wikipage to another Wikipage of
is Wikipage redirect of
is foaf:primaryTopic of
Faceted Search & Find service v1.17_git139 as of Feb 29 2024


Alternative Linked Data Documents: ODE     Content Formats:   [cxml] [csv]     RDF   [text] [turtle] [ld+json] [rdf+json] [rdf+xml]     ODATA   [atom+xml] [odata+json]     Microdata   [microdata+json] [html]    About   
This material is Open Knowledge   W3C Semantic Web Technology [RDF Data] Valid XHTML + RDFa
OpenLink Virtuoso version 08.03.3331 as of Sep 2 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (62 GB total memory, 54 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software