DOCUMENTA MATHEMATICA, Quadratic Forms LSU (2001), 201-218

Max-Albert Knus and Oliver Villa

Quadratic Quaternion Forms, Involutions and Triality

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.

2000 Mathematics Subject Classification: 11E39, 11E88

Keywords and Phrases: Quadratic quaternion forms, Involutions, Triality

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