$(2+1)$-dimensional quantum gravity noncommutative spacetime geometry and deformations of Poincaré symmetry arise naturally, recently the $\kappa$-deformation in $(2+1)$ dimensions has attracted quite some attention as well, see e.g. [@Ballesteros3dim1; @Ballesteros3dim2; @Ballesteros3dim3; @Matschull; @Schroers-Meusb]. In [@BP_unif] the deformation of the symmetry algebra (i.e. generalized for any $\tau$ the $\kappa$-deformed inhomogeneous orthogonal Hopf algebra $U_{\kappa,\tau}(\operatorname{iso}(g))$) was determined by a metric tensor $g$ of any dimension and arbitrary signature. Such formulation allows for many applications within the deformed general relativity and Planck scale physics, including $(2+1)$-dimensional case allowing for relation with quantum gravity models. The deformation of inhomogeneous orthogonal algebras corresponding to $\kappa (\tau)$-Minkowski spacetime explicitly depends on the choice of an additional vector field $\tau$ which at the same time parameterizes classical $r$-matrices and distinguishes between nonequivalent deformations[^1].

In this paper we want to focus on mathematical issues connected with this generalized $\kappa (\tau)$- deformation and discuss related problems. The framework of Drinfel’d type of deformations [@Drinfeld1; @Drinfeld3] requires the so-called $h$-adic topology [@ChP; @Klimyk], i.e. dealing with formal power series therefore one usually uses in fact topological completion $U(\operatorname{iso}(g))[[\frac{1}{\kappa}]]$. The version of $\kappa$-Poincaré algebra used by many authors [@LNR; @Luk1; @Luk2; @MR] in a traditional approach is (implicitly) of such ‘$h$-adic’ 