Automorphisms and quasiconformal mappings of Heisenberg-type groups.

Title: Automorphisms and quasiconformal mappings of Heisenberg-type groups.
Identifier: AAI9521247
identifier: 9521247
Creator: Barbano, Paolo Emilio.
Contributor: Adviser: Martin Moskowitz
Date: 1995
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: The Lie algebras of derivations of trace-zero of Heisenberg-type groups are explicitly computed, along with the connected component of the group of isometries of an H-type Lie group with the metric invariant under left translations and certain automorphisms defined by A. Koranyi (18). Using this we prove a result on stabilizers of lattices and give a necessary and sufficient condition for the existence of non-conformal quasi-conformal mappings. The latter shows that except for the abelian and Heisenberg cases, all quasi-conformal mappings must actually be conformal. A characterization of the isometry group of solvable extensions of H-type groups is also given. Finally we show an application of these techniques to prove that in certain rank-one Lie groups all non-uniform lattices are arithmetic. The last chapter is dedicated to the study of the {dollar}L\sp1{dollar}-algebras and representation theory of quaternionic Lie groups of Heisenberg-type.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.