  We consider those projective bundles (or Brauer-Severi varieties) over an
abelian variety that are homogeneous, i.e., invariant under translation. We
describe the structure of these bundles in terms of projective representations
of commutative algebraic groups; the irreducible bundles correspond to
Heisenberg groups and their standard representations. Our results extend those
of Mukai on semi-homogeneous vector bundles, and yield a geometric view of the
Brauer group of abelian varieties.
