  An alternative (simplified) derivation of the dispersion relation and the
expressions for the momentum-energy 4-vector $p_i,p_0$ given initially in [1]
is provided. It has turned out that in a rather "pedestrian" manner one can
obtain in one stroke not only the above relations but also the correct
dispersion relation in $\omega-k_i$ space, consistent with the value of a
velocity of a massless particle. This is achieved by considering the standard
Lorentz algebra for $\omega-k_i$-space. A non-uniqueness of the choice of the
time-derivative in the presence of the finite length scale is discussed. It is
shown that such non-uniqueness does not affect the dispersion relation in
$\omega-k_i$-space. albeit results in different dispersion relations in
$p-p_0$-space depending on the choice of the definition of the time derivative.
