Linkage of quadratic Pfister forms

Adam Chapman; Shira Gilat; Uzi Vishne

doi:10.1080/00927872.2017.1298776

Linkage of quadratic Pfister forms

Adam Chapman
, Shira Gilat
, Uzi Vishne

Department of Mathematics

Tel Hai Academic College

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We study the necessary conditions for sets of quadratic n-fold Pfister forms to have a common (n−1)-fold Pfister factor. For any set S of n-fold Pfister forms generating a subgroup of Iⁿ _qF/Iⁿ⁺¹ _qF of order 2^s in which every element has an n-fold Pfister representative, we associate an invariant in Iⁿ⁺¹ _qF which lives inside I^n+s−1 _qF when the forms in S have a common (n−1)-fold Pfister factor. We study the properties of this invariant and compute it explicitly in a few interesting cases.

Original language	English
Pages (from-to)	5212-5226
Number of pages	15
Journal	Communications in Algebra
Volume	45
Issue number	12
DOIs	https://doi.org/10.1080/00927872.2017.1298776
State	Published - 2 Dec 2017

Bibliographical note

Publisher Copyright:
© 2017 Taylor & Francis.

Keywords

Linkage
Pfister forms
quadratic forms
quaternion algebras

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10.1080/00927872.2017.1298776

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abstract = "We study the necessary conditions for sets of quadratic n-fold Pfister forms to have a common (n−1)-fold Pfister factor. For any set S of n-fold Pfister forms generating a subgroup of In qF/In+1 qF of order 2s in which every element has an n-fold Pfister representative, we associate an invariant in In+1 qF which lives inside In+s−1 qF when the forms in S have a common (n−1)-fold Pfister factor. We study the properties of this invariant and compute it explicitly in a few interesting cases.",

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AU - Gilat, Shira

AU - Vishne, Uzi

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AB - We study the necessary conditions for sets of quadratic n-fold Pfister forms to have a common (n−1)-fold Pfister factor. For any set S of n-fold Pfister forms generating a subgroup of In qF/In+1 qF of order 2s in which every element has an n-fold Pfister representative, we associate an invariant in In+1 qF which lives inside In+s−1 qF when the forms in S have a common (n−1)-fold Pfister factor. We study the properties of this invariant and compute it explicitly in a few interesting cases.

KW - Linkage

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KW - quaternion algebras

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JO - Communications in Algebra

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Linkage of quadratic Pfister forms

Abstract

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Keywords

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