Automorphisms and quasi-conformal mappings of Heisenberg type groups

Abstract: 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.

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