Ulrich bundles on Brauer–Severi varieties

We prove the existence of Ulrich bundles on any Brauer–Severi variety. In some cases, the minimal possible rank of the obtained Ulrich bundles equals the period of the Brauer–Severi variety. Moreover, we find a formula for the rank of an Ulrich bundle involving the period of the considered Brauer–Severi variety X X , at least if d i m ( X ) = p − 1 \mathrm {dim}(X)=p-1 for an odd prime p p . This formula implies that the rank of any Ulrich bundle on such a Brauer–Severi variety X X must be a multiple of the period.