  Non Abelian geometric phases are attracting increasing interest because of
possible experimental application in quantum computation. We study the effects
of the environment (modelled as an ensemble of harmonic oscillators) on a
holonomic transformation and write the corresponding master equation. The
solution is analytically and numerically investigated and the behavior of the
fidelity analyzed: fidelity revivals are observed and an optimal finite
operation time is determined at which the gate is most robust against noise.
