Abstract and Applied Analysis
Volume 2013 (2013), Article ID 645848, 5 pages
http://dx.doi.org/10.1155/2013/645848
Research Article

On the Homomorphisms of the Lie Groups and

Fatma Özdemir1 and Hasan Özekes2

1Department of Mathematics, Faculty of Science and Letters, Istanbul Technical University, Maslak, 34469 Istanbul, Turkey
2Department of Mathematics, Faculty of Science and Letters, Okan University, 34959 Istanbul, Turkey

Received 14 February 2013; Revised 1 April 2013; Accepted 7 April 2013

Academic Editor: Nail Migranov

Copyright © 2013 Fatma Özdemir and Hasan Özekes. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We first construct all the homomorphisms from the Heisenberg group to the 3-sphere. Also, defining a topology on these homomorphisms, we regard the set of these homomorphisms as a topological space. Next, using the kernels of homomorphisms, we define an equivalence relation on this topological space. We finally show that the quotient space is a topological group which is isomorphic to .