Abstract and Applied Analysis

On the Homomorphisms of the Lie Groups $SU(2)$ and ${S}^{3}$

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 ${\mathrm{\Bbb S}}^{1}$.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 645848, 5 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393444221

Digital Object Identifier
doi:10.1155/2013/645848

Mathematical Reviews number (MathSciNet)
MR3055861

Zentralblatt MATH identifier
1275.53046

Citation

Özdemir, Fatma; Özekes, Hasan. On the Homomorphisms of the Lie Groups $SU(2)$ and ${S}^{3}$. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 645848, 5 pages. doi:10.1155/2013/645848. https://projecteuclid.org/euclid.aaa/1393444221

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