  The construction of Lie bialgebra from double Lie algebra is presented. It is
used to relate some types of cobracket on inhomogenous so(p,q) algebras with
double Lie algebra structures on so(p+1,q) or so(p,q+1). Also it is shown that
the cobracket corresponding to kappa-deformation gives rise to complete
Poisson-Lie Euclidean groups and non-complete Poincare groups.
