  In the recently proposed extension of the YM theory, non-Abelian tensor gauge
field of the second rank is represented by a general tensor whose symmetric
part describes the propagation of charged gauge boson of helicity two and its
antisymmetric part - the helicity zero charged gauge boson. On the
non-interacting level these polarizations are similar to the polarizations of
the graviton and of the Abelian antisymmetric B field, but the interaction of
these gauge bosons carrying non-commutative internal charges cannot be directly
identified with the interaction of gravitons or B field. Our intention here is
to illustrate this result from different perspectives which would include
Bianchi identity for the corresponding field strength tensor and the analysis
of the second-order partial differential equation which describes in this
theory the propagation of non-Abelian tensor gauge field of the second rank.
