Anne Quéguiner-Mathieu, Jean-Pierre Tignol: Discriminant and Clifford Algebras,

Submission: 2001, Feb 8

The centralizer of a square-central skew-symmetric unit in a central simple algebra with orthogonal involution carries a unitary involution. The discriminant algebra of this unitary involution is shown to be an orthogonal summand in one of the components of the Clifford algebra of the orthogonal involution. As an application, structure theorems for orthogonal involutions on central simple algebras of degree 8 are obtained.

2000 Mathematics Subject Classification: 11E39, 11E57, 16K20

Keywords and Phrases: central simple algebra with involution, Clifford algebra

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