Date of Award

8-1-2017

Degree Name

Master of Science

Department

Mathematics

First Advisor

Kocik, Jerzy

Abstract

There are four division algebras namely, real numbers, complex numbers, quaternions and octonions. They can be used to represent a number of orthogonal groups. In particular, the groups SO(3) and SO(4) of rotations of 3- and 4-dimensional spaces, respectively, can be described in terms of quaternions. We start with reviewing these cases and next turn to the groups of rotations of 7- and 8- dimensional spaces and describe them in terms of octonions. Since octonions form a non-associative division algebra, we use Moufang Identities to overcome the difficulty of some calculations and provide transformations that generate groups SO(7) and SO(8), which is an alternative description for these orthogonal groups.

Share

COinS
 

Access

This thesis is only available for download to the SIUC community. Current SIUC affiliates may also access this paper off campus by searching Dissertations & Theses @ Southern Illinois University Carbondale from ProQuest. Others should contact the interlibrary loan department of your local library or contact ProQuest's Dissertation Express service.