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Orthogonal involutions and totally singular quadratic forms in characteristic two

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Abstract

We associate to every central simple algebra with involution of orthogonal type in characteristic two a totally singular quadratic form which reflects certain anisotropy properties of the involution. It is shown that this quadratic form can be used to classify totally decomposable algebras with orthogonal involution. Also, using this form, a criterion is obtained for an orthogonal involution on a split algebra to be conjugated to the transpose involution.

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  1. Department of Pure Mathematics, Faculty of Science, University of Kashan, P. O. Box 87317-51167, Kashan, Iran

    A.-H. Nokhodkar

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  1. A.-H. Nokhodkar
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Nokhodkar, AH. Orthogonal involutions and totally singular quadratic forms in characteristic two. manuscripta math. 154, 429–440 (2017). https://doi.org/10.1007/s00229-017-0922-y

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  • DOI: https://doi.org/10.1007/s00229-017-0922-y

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