  A new Hamiltonian structure of the Maxwell-Bloch equations is described. In
this setting the Maxwell-Bloch equations appear as a member of a family of
generalized Maxwell-Bloch systems. The family is parameterized by compact
semi-simple Lie groups, the original Maxwell-Bloch system being the member
corresponding to SU(2). The Hamiltonian structure is then used in the
construction of a new family of symmetries and the associated conserved
quantities of the Maxwell-Bloch equations.
