Pfister involutions
نویسندگان
چکیده
منابع مشابه
Pfister Involutions
The question of the existence of an analogue, in the framework of central simple algebras with involution, of the notion of Pfister form is raised. In particular, algebras with orthogonal involution which split as a tensor product of quaternion algebras with involution are studied. It is proven that, up to degree 16, over any extension over which the algebra splits, the involution is adjoint to...
متن کاملPfister ’ S Theorem for Involutions Of
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. In his seminal paper [Pf], Pfister proved strong theorems describing quadratic forms of even dimension ≤ 12 that have trivial discriminant and Clifford invariant, i.e., that are in I 3. His results have been e...
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We show that over a field of characteristic 2 a central simple algebra with orthogonal involution that decomposes into a product of quaternion algebras with involution is either anisotropic or metabolic. We use this to define an invariant of such orthogonal involutions in characteristic 2 that completely determines the isotropy behaviour of the involution. We also give an example of a non-total...
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The question of which quadratic forms become isotropic when extended to the function field of a given form is studied. A formula for the minimum dimension of the minimal isotropic forms associated to such extensions is given, and some consequences thereof are outlined. Especial attention is devoted to function fields of Pfister forms. Here, the relationship between excellence concepts and the i...
متن کاملSquare Involutions
A square involution is a square permutation which is also an involution. In this paper we give the enumeration of square involutions, using purely combinatorial methods, by establishing a bijective correspondence with a class of lattice paths. As a corollary to our result, we enumerate various subclasses of square involutions, including the classes of triangular, decomposable, and fat involutions.
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ژورنال
عنوان ژورنال: Proceedings Mathematical Sciences
سال: 2003
ISSN: 0253-4142,0973-7685
DOI: 10.1007/bf02829631