Finiteness of Hermitian Levels of Some Algebras

Abstract

We characterize the hermitian levels of quaternion and octonion algebrasand of an 8-dimensional algebra D over the ground field F, constructed using a weak version of the Cayley-Dickson double process.It is shown that all values of the hermitian levels of quaternion algebras with the hat-involution also occur as hermitian levels of D. We give some limits to the levels of the algebra D over some ground field.

Keywords

• KeyWords:Quaternion algebra
• octonion algebra
• level
• hermitian level
• sums of squares
• quadratic forms.