Symbol algebras, involutions and trace forms
Ronan Flatley · Irish Mathematical Society Bulletin · 2012
Let n be an arbitrary positive integer and let K be a field of characteristic different from 2 containing a primitive n th root of unity . Let a, b K and S be the algebra over K generated by elements x and y subject to the relations x n = a, y n = b and yx = xy. We call S a symbol algebra. Symbol algebras are central simple algebras and are generalisations of quaternion algebras. We construct examples of symbol algebras of arbitrary degree.