Submission: 2001, Jul 11
Pfister forms play a prominent role in the algebraic theory of quadratic forms. On the other hand, involutions on central simple algebras share many properties with quadratic forms. Hence it is natural to look for an analog of the notion of Pfister form in the framework of algebras with involution. The aim of the present paper is to propose such a notion. An $n$--fold Pfister involution (or Pfister involution, for short) will be by definition a central simple algebra with an orthogonal involution which is a tensor product of $n$ quaternion algebras with involution. We show that if $n = 4$, then after passing to any splitting field of the algebra, the involution is induced by a Pfister form. For $n\le 3$, this was already proved by D. Tao. We also compute cohomological invariants of $2$-fold Pfister involutions, and raise some open questions.
2000 Mathematics Subject Classification:
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