queguin@math.univ-paris13.fr

Submission: 2009, Feb 6

Izhboldin and Karpenko proved in 2000 that any quadratic form of dimension $8$ with trivial discriminant and Clifford algebra of index $4$ is isometric to the transfer, with respect to some quadratic étale extension, of a quadratic form similar to a two-fold Pfister form. We give a new proof of this result, based on a theorem of decomposability for degree $8$ and index $4$ algebras with orthogonal involution.

2000 Mathematics Subject Classification: 11E04, 16K20 (16W10)

Keywords and Phrases: Quadratic forms ; Algebras with involutions ; Clifford algebras ; Decomposability

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