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  1. On Hermitian Pfister forms
On Hermitian Pfister forms
678 viewed

On Hermitian Pfister forms

Grenier Boley, N

On Hermitian Pfister forms

Grenier Boley, N ; Sharif University of Technology | 2008

678 Viewed
  1. Type of Document: Article
  2. DOI: 10.1142/S021949880800303X
  3. Publisher: 2008
  4. Abstract:
  5. Let K be a field of characteristic different from 2. It is known that a quadratic Pfister form over K is hyperbolic once it is isotropic. It is also known that the dimension of an anisotropic quadratic form over K belonging to a given power of the fundamental ideal of the Witt ring of K is lower bounded. In this paper, weak analogues of these two statements are proved for hermitian forms over a multiquaternion algebra with involution. Consequences for Pfister involutions are also drawn. An invariant uα of K with respect to a nonzero pure quaternion of a quaternion division algebra over K is defined. Upper bounds for this invariant are provided. In particular an analogue is obtained of a result of Elman and Lam concerning the u-invariant of a field of level at most 2. © 2008 World Scientific Publishing Company
  6. Keywords:
  7. Hermitian form ; Pfister form ; multiquaternion algebra with involution ; Pfister involution ; u-invariant
  8. Source: Journal of Algebra and its Applications ; Volume 7, Issue 5 , 2008 , Pages 629-645 ; 02194988 (ISSN)
  9. URL: https://www.worldscientific.com/doi/10.1142/S021949880800303X