منابع مشابه
Isotropy of Orthogonal Involutions
An orthogonal involution on a central simple algebra becoming isotropic over any splitting field of the algebra, becomes isotropic over a finite odd degree extension of the base field (provided that the characteristic of the base field is not 2). Our aim is a proof of the following result, generalizing the hyperbolicity statement of [5]: Theorem 1. Let F be a field of characteristic not 2, A a ...
متن کاملHyperbolicity of Orthogonal Involutions
We show that a non-hyperbolic orthogonal involution on a central simple algebra over a field of characteristic 6= 2 remains non-hyperbolic over some splitting field of the algebra.
متن کاملOn Anisotropy of Orthogonal Involutions
We show that an orthogonal involution of a central division algebra D (over a field of characteristic not 2) remains anisotropic over the generic splitting field of D. We also give a couple of other applications of the same technique.
متن کاملOrthogonal Pfister Involutions in Characteristic Two
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...
متن کاملInvolutions of a Clifford algebra induced by involutions of orthogonal group in characteristic 2
Among the involutions of a Clifford algebra, those induced by the involutions of the orthogonal group are the most natural ones. In this work, several basic properties of these involutions, such as the relations between their invariants, their occurrences and their decompositions are investi-
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 2013
ISSN: 1080-6377
DOI: 10.1353/ajm.2013.0011