Finiteness of hermitian levels of some algebras - Dos Santos, Clotilzio Moreira [UNESP] (Sociedade Paranaense de Matemática, 2011)
We characterize the hermitian levels of quaternion and octonion algebras and 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. © Soc. Paran. de Mat.
Keywords: Hermitian level; Level; Octonion algebra; Quadratic forms; Quaternion algebra; Sums of squares