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Archiv der Mathematik

, Volume 110, Issue 3, pp 213–224 | Cite as

Subforms of norm forms of octonion fields

  • Norbert Knarr
  • Markus J. StroppelEmail author
Article

Abstract

We characterize the forms that occur as restrictions of norm forms of octonion fields. The results are applied to forms of types E\(_6\), E\(_7\), and E\(_8\) and to positive definite forms over fields that allow a unique non-split octonion algebra, e.g., the field of rational numbers.

Keywords

Quadratic form Similitude Octonion Quaternion Composition algebra Division algebra Form of type E\(_6\) Form of type E\(_7\) Form of type E\(_8\) 

Mathematics Subject Classification

11E04 17A75 

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Notes

Acknowledgements

The authors thank an anonymous referee for pointing out that 4.3.3 follows in the context of our present results.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.LExMath, Fakultät für Mathematik und PhysikUniversität StuttgartStuttgartGermany

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