Quadratic Quaternion Forms, Involutions and Triality

Villa, Oliver and Knus, Max-Albert (2001) Quadratic Quaternion Forms, Involutions and Triality. Documenta Mathematica. pp. 201-218. ISSN 1431-0643

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Quadratic quaternion forms, introduced by Seip-Hornix (1965), are special cases of generalized quadratic forms over algebras with involutions. We apply the formalism of these generalized quadratic forms to give a characteristic free version of different results related to hermitian forms over quaternions: 1) An exact sequence of Lewis 2) Involutions of central simple algebras of exponent 2. 3) Triality for 4-dimensional quadratic quaternion forms.

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