Pfister form (original) (raw)
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.
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| dbo: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) |
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| 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) |
| rdfs:label | Pfister form (en) |
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