  We consider a family of non-commutative 4d Minkowski spaces with the
signature (1,3) and two types of spaces with the signature (2,2). The Minkowski
spaces are defined by the common reflection equation and differ in
anti-involutions. There exist two Casimir elements and the fixing of one of
them leads to non-commutative "homogeneous" spaces $H_3$, $dS_3$, $AdS_3$ and
light-cones. We present the quasi-classical description of the Minkowski
spaces. There are three compatible Poisson structures - quadratic, linear and
canonical. The quantization of the former leads to the considered Minkowski
spaces. We introduce the horospheric generators of the Minkowski spaces. They
lead to the horospheric description of $H_3$, $dS_3$ and $AdS_3$. The
irreducible representations of Minkowski spaces $H_3$ and $dS_3$ are
constructed. We find the eigen-functions of the Klein-Gordon equation in the
terms of the horospheric generators of the Minkowski spaces. They give rise to
eigen-functions on the $H_3$, $dS_3$, $AdS_3$ and light-cones.
