in a triangular case: as an intermediate step one needs to construct a twisting element before quantizing. Twisting two-tensors corresponding to Zakrzewski’s scheme have been already found in [@Tol0704.0081a; @Tol0704.0081b] (see also [@BLT4; @BLT3; @BLT2; @BLT1; @LL-0406155; @Lyakhovsky]). Here we use such twists (corresponding to the extended classical $r$-matrices) in order to deform $\kappa(\tau)$-Minkowski spacetime algebra and describe resulting algebras in terms of solvable Lie algebras. To this aim we use classification scheme of low-dimensional solvable Lie algebras proposed in [@Graaf]. As a final task in this paper we calculate the deformed coproducts for some selected twistings of the $\kappa$-deformations. It turns out that the possibility of their specialization is related with the type of twisted $\kappa$-Minkowski spacetime algebras.

$\boldsymbol{\kappa(\tau)}$-deformations for (inhomogeneous) orthogonal\
Lie algebras
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Here we recall the form of $\kappa$-deformations recently written in an unified way [@BP_unif]. Let $V$ be a $D$-dimensional (real) vector space equipped with a metric tensor $g$ of arbitrary signature $(p, q)$, $p+q=D$. For an arbitrary basis $\{e_{\mu}\}_{\mu=0}^{D-1}$ one can introduce its components $g_{\mu
\nu}=g(e_{\mu},e_{\nu})$. Making use of the dual basis $\{e^{\mu}\}_{\mu=0}^{D-1}$ in the dual vector space $V^\#$ one can write $g=g_{\alpha\beta}e^\alpha\otimes e^\beta$. It is well-known that Lie algebra of inhomogeneous orthogonal group 