Let D d =(a,b/F) a quaternion divisior algebra over a field F of characteristic #x2208; 2. Denote 1, i, j , k the basis of D, such that i2d n, j2d b, ij d -ji d k and A :D #x2192; D the involution given by i d -i, j d j (and k d k). In LE D. LEWIS asks the following question :Does there exist a quadratic Pfister form S p. 721 d such that the hermitian form d d D is isotropic over (D, d) but not hyperbolic amp; In this note, we show that the answer of this question is negative, so that the hermitien level #xA7;I, when it is finite, of (D, A) is a power of two. This result holds for quaternion algebras with standard involution LE.
展开▼
