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APPLICATIONS OF SYSTEMS OF QUADRATIC FORMS TO GENERALISED QUADRATIC FORMS

Part of: Forms and linear algebraic groups Field extensions

Published online by Cambridge University Press:  13 February 2020

A.-H. NOKHODKAR Open the ORCID record for A.-H. NOKHODKAR [Opens in a new window]
A.-H. NOKHODKAR*
Affiliation:
Department of Pure Mathematics, Faculty of Science, University of Kashan, PO Box 87317-51167, Kashan, Iran email a.nokhodkar@kashanu.ac.ir
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Abstract

A system of quadratic forms is associated to every generalised quadratic form over a division algebra with involution of the first kind in characteristic two. It is shown that this system determines the isotropy behaviour and the isometry class of generalised quadratic forms. An application of this construction to the Witt index of generalised quadratic forms is also given.

Keywords

generalised quadratic formsystem of quadratic formsWitt indexdivision algebra with involution

MSC classification

Primary: 11E04: Quadratic forms over general fields
Secondary: 11E39: Bilinear and Hermitian forms 12F10: Separable extensions, Galois theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 102 , Issue 3 , December 2020 , pp. 374 - 386
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

This research is partially supported by the University of Kashan under Grant No. 890193/1.

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