  In this article we present a new C*-algebraic deformation of the Lorentz
group. It is obtained by means of the Rieffel deformation applied to SL(2,C).
We give a detailed description of the resulting quantum group in terms of
generators - the quantum counterparts of the matrix coefficients of the
fundamental representation of SL(2,C). In order to construct the most involved
of four generators, we first define it on the quantum Borel subgroup, then on
the quantum complement of the Borel subgroup and finally we perform the gluing
procedure. In order to classify representations of the C*-algebra of the
Heisenberg-Lorentz quantum group and to analyze the action of the
comultiplication on the generators we employ the duality in the theory of
locally compact quantum groups.
