20 09 Heisenberg - Lorentz Quantum Group

In this article we present a new deformation of SL(2,C) on the C∗-algebra level. The method of its construction is the Rieffel deformation. We give a detailed description of so obtained a quantum group (A,∆) in terms of affiliated elements α̂, β̂, γ̂, δ̂ ∈ A generating A. In order to construct β̂, we split A onto parts on which β̂ can easily be defined and then show that gluing procedure can be performed. Using the duality for locally compact quantum groups we were able to describe all representations of the C∗-algebra A and to analyze the action of ∆ on generators α̂, β̂, γ̂, δ̂.