Pfister's Theorem for orthogonal involutions of degree $12$

Skip Garibaldi (1) , Anne Quéguiner-Mathieu (2)

1 Department of Mathematics and Computer Science [Emory University]
2 LAGA - Laboratoire Analyse, Géométrie et Applications

We use the fact that a projective half-spin representation of $Spin_{12}$ has an open orbit to generalize Pfister's result on quadratic forms of dimension $12$ in $I^3$ to orthogonal involutions.

Mots clés: Algebraic groups; Algebras with involution; Quadratic Forms

Domaines: Anneaux et algèbres [math.RA]; Théorie des groupes [math.GR]

Skip Garibaldi, Anne Quéguiner-Mathieu. Pfister's Theorem for orthogonal involutions of degree $12$. 2007. ⟨hal-00250039⟩