No full exceptional collections on non-split Brauer--Severi varieties of   dimension $\leq 3$
  In an earlier paper we showed that non-split Brauer--Severi curves do not admit full strong exceptional collections. In the present note we extend this observation and prove that there cannot exist full exceptional collections on non-split Brauer--Severi varieties of dimension $\leq 3$. 
Sa\v{s}a Novakovi\'c
math.AG