  We study the effects of rotation on the dynamics, energetics and Ni-56
production of Pair Instability Supernova explosions by performing rotating
two-dimensional ("2.5-D") hydrodynamics simulations. We calculate the evolution
of eight low metallicity (Z = 10^-3, 10^-4 Zsun) massive (135-245 Msun) PISN
progenitors with initial surface rotational velocities 50% that of the critical
Keplerian value using the stellar evolution code MESA. We allow for both the
inclusion and the omission of the effects of magnetic fields in the angular
momentum transport and in chemical mixing, resulting in slowly-rotating and
rapidly-rotating final carbon-oxygen cores, respectively. Increased rotation
for carbon-oxygen cores of the same mass and chemical stratification leads to
less energetic PISN explosions that produce smaller amounts of Ni-56 due to the
effect of the angular momentum barrier that develops and slows the dynamical
collapse. We find a non-monotonic dependence of Ni-56 production on rotational
velocity in situations when smoother composition gradients form at the outer
edge of the rotating cores. In these cases, the PISN energetics are determined
by the competition of two factors: the extent of chemical mixing in the outer
layers of the core due to the effects of rotation in the progenitor evolution
and the development of angular momentum support against collapse. Our 2.5-D
PISN simulations with rotation are the first presented in the literature. They
reveal hydrodynamic instabilities in several regions of the exploding star and
increased explosion asymmetries with higher core rotational velocity.
