Automophisms and Quasi-Conformal Mappings of Heisenberg Type Groups

The Lie algebras of trace-zero derivations of Heisenberg-type groups are explicitly characterized, along with the connected component of their groups of measure preserving automorphisms.We establish a general criterion on properties of the stabilizer of a lattice in a simply connected nilpotent Lie group and apply it to the full family of H -type Lie groups.A necessary condition for the existence of non-conformal quasi-conformal mappings on H -type groups is also given.