  We propose a generalized description for the kappa-Poincare-Hopf algebra as a
symmetry quantum group of underlying kappa-Minkowski spacetime. We investigate
all the possible implementations of (deformed) Lorentz algebras which are
compatible with the given choice of kappa-Minkowski algebra realization. For
the given realization of kappa-Minkowski spacetime there is a unique
kappa-Poincare-Hopf algebra with undeformed Lorentz algebra. We have
constructed a three-parameter family of deformed Lorentz generators with
kappa-Poincare algebras which are related to kappa-Poincare-Hopf algebra with
undeformed Lorentz algebra. Known bases of kappa-Poincare-Hopf algebra are
obtained as special cases. Also deformation of igl(4) Hopf algebra compatible
with the kappa-Minkowski spacetime is presented. Some physical applications are
briefly discussed.
