Finiteness of Hermitian Levels of some Algebras - doi: 10.5269/bspm.v29i2.12850
DOI:
https://doi.org/10.5269/bspm.v29i2.12850Keywords:
Quaternion algebra, octonion algebra, level, hermitian level, sums of squares, quadratic forms.Abstract
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.
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