ON THE LEVEL OF A QUATERNION ALGEBRA
Ahmed Laghribi, Pasquale Mammone · Communications in Algebra · 2001
In [6] Lewis, D. W. 1989. Levels of quaternions algebras. Rocky Mountain J., 19: 787–792. [Google Scholar] D. W. Lewis proved the existence of a quaternion division algebra of level 2 n or 2 n + 1 for any integer n ≥ 1. In this note, we present news examples of quaternion division algebras of such levels. We also recover a result of P. Koprowski [4] Koprowski, P. 1998. Sums of squares of pure quaternions. Proc. Royal Irish Acad., [Google Scholar]. Our method is different and based on function field of projective quadrics.