type. In this approach the deformation parameter $\kappa$ cannot take a numerical value and must stay formal which makes it difficult to undergo some physical interpretation, e.g., as Planck mass or quantum gravity scale. Nevertheless there exists a method which in some cases allows deformation parameter to take a constant (numerical) value. In this sense the $\kappa$-Poincaré quantum group with $h$-adic topology as described before [@koma95; @LLM; @LNR; @Luk1; @Luk2; @MR; @Z], is not the only possible version. In this paper we will reformulate this traditional Hopf algebra to hide the infinite series on the abstract level. This is known to be always possible in the framework of Drinfel’d–Jimbo standard quantization of semi-simple Lie algebras. As a first step, one distinguishes certain sub-Hopf algebra which can be treated as a Hopf algebra over polynomial ring $\mathbb{C}[q,q^{-1}]$ (the so called ‘$q$-analog’ version), in this way, getting rid off $h$-adic topology. Next we create new Hopf algebra by setting up (specializing) the formal parameter $q$ to some numerical (complex in general) value. As a result, one obtains a one-parameter family of new Hopf algebras labeled by the numerical parameter which (when real) could be interpreted as some physical quantity. Usually, the value 