  The preprint is prepared as description of results that were obtained during
joint scientific project No: 71NC /2015/VNCCCT on the VIASM (Vietnam Institute
for Advanced Study in Mathematics) from 08.12.2015 to 06.02.2016.
  The problem was formulated how to calculate so called the Mackenzie
obstruction for existing of transitive Lie algebroid for given coupling between
a finite dimensional Lie algebra and the tangent bundle of a smooth manifold.
  It is proved that the Mackenzie obstruction for transitive Lie algebroids is
trivial for the finite dimensional Lie algebra which is the direct sum of the
center and the subalgebra without the center.
