Record Details
The geometry of the octonionic multiplication table
ScholarsArchive at Oregon State University
| Field | Value |
|---|---|
| Title | The geometry of the octonionic multiplication table |
| Names |
Killgore, Peter Lloyd
(creator) Dray, Tevian (advisor) |
| Date Issued | 2015-05-15 (iso8601) |
| Note | Honors Bachelor of Science (HBS) |
| Abstract | We analyze some symmetries of the octonionic multiplication table, expressed in terms of the Fano plane. In particular, we count how many ways the Fano plane can be labeled as the octonionic multiplication table, all corresponding to a specified octonion algebra. We show that only 28 of these labelings of the Fano plane are nonequivalent, which leads us to consider the automorphism group of the octonions. Specifically, we look at the case when the mapping between two labelings of the Fano plane is an automorphism. Each such automorphism is induced by a permutation, and we argue that only 21 such automorphisms exist. We give the explicit definition of all 21 automorphisms and determine the structure of the group they generate. Finally, we interpret our results in a geometric context, noting especially the connection to the 7-dimensional cross product. |
| Genre | Thesis |
| Access Condition | http://creativecommons.org/licenses/by-nd/3.0/us/ |
| Topic | Octonions |
| Identifier | http://hdl.handle.net/1957/55902 |
