Singular and Totally Singular Unitary Spaces

Abstract

In this article, we present a decomposition theorem for unitary spaces over a central simple division algebra with involution in characteristic 2. This is a generalization of a decomposition result for quadratic forms in characteristic 2 from [4] and extends a generalization of the Witt decomposition theorem for nonsingular spaces in this setting to cover spaces that may be singular.

Key Words:

• Central simple algebras
• Characteristic two
• Generalised quadratic forms
• Involutions
• Unitary spaces
• Witt decomposition

2010 Mathematics Subject Classification:

• 11E39
• 11E81
• 12F05
• 12F10

ACKNOWLEDGMENTS

I would like to thank the reviewer for the careful reading of the manuscript and for suggestions that improved the content and clarity for this article a great deal.

Notes

Communicated by A. Wadsworth.