ON THE LEVEL OF A QUATERNION ALGEBRA

In [6] 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]. Our method is different and based on function field of projective quadrics.