Involutions of a Clifford Algebra Induced by Involutions of Orthogonal Group in Characteristic 2

Abstract

Among the involutions of a Clifford algebra, those induced by the involutions of the orthogonal group are the most natural ones. In this work, several basic properties of these involutions, such as the relations between their invariants, their occurrences, and their decompositions, are investigated.

Key Words:

• Bilinear and quadratic forms
• Clifford algebras
• Involutions
• Orthogonal group
• Reflections

2010 Mathematics Subject Classification:

• 11E88
• 11E04
• 16W10

ACKNOWLEDGMENTS

We thank the referee for careful reading of the manuscript and for some useful suggestions.

Notes

Communicated by A. Wadsworth.