Dissipative "Groups" and the Bloch Ball
  We show that a quantum control procedure on a two-level system including dissipation gives rise to a semi-group corresponding to the Lie algebra semi-direct sum gl(3,R)+R^3. The physical evolution may be modelled by the action of this semi-group on a 3-vector as it moves inside the Bloch sphere, in the Bloch ball. 
Allan I. Solomon and Sonia G. Schirmer (Quantum Processes Group, Open   University and DAMTP, Cambridge)