Browsing College of Science by Subject "Quadratic form"

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Bounds on the levels of composition algebras

O'Shea, James (Royal Irish Academy, 2010)

Certain families of quaternion and octonion algebras are conjectured to be of level and sublevel n. A proof of this conjecture is offered in the case where n is a power of two. Hoffmann's proof of the existence of infinitely ...
Levels and sublevels of composition algebras

O'Shea, James (Elsevier, 2007)

Lewis' and Leep's bounds on the level and sublevel of quaternion algebras are extended to the class of composition algebras. Some simple constructions of composition algebras of known level values are given. In addition, ...
Levels and sublevels of composition algebras over p-adic function fields

O'Shea, James ; Geel, Jan Van (Birkhäuser, 2008)

In [O'S], the level and sublevel of composition algebras are studied, wherein these quantities are determined for those algebras defined over local fields. In this paper, the level and sublevel of composition algebras, of ...
The Procesi-Schacher conjecture and Hilbert’s 17th problem for algebras with involution

Klep, Igor ; Unger, Thomas (Elsevier, 2010-07)

In 1976 Procesi and Schacher developed an Artin–Schreier type theory for central simple algebras with involution and conjectured that in such an algebra a totally positive element is always a sum of hermitian squares. In ...