Algebras with involution that become hyperbolic over the fonction field of a conic

Details Algebras with involution that become hyperbolic over the fonction field of a conic Algebras with involution that become hyperbolic over the fonction field of a conic

2008-05-27

arxiv.org/abs/0805.4138v1

Mathematics

Rings and Algebras

Scientific paper

We study central simple algebras with involution of the first kind that become hyperbolic over the function field of the conic associated to a given quaternion algebra $Q$. We classify these algebras in degree~4 and give an example of such a division algebra with orthogonal involution of degree~8 that does not contain $Q$ with its canonical involution, even though it contains $Q$ and is totally decomposable into a tensor product of quaternion algebras with involution.

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