The geometry of the octonionic multiplication table

Honors College Thesis

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Citeable URL: https://ir.library.oregonstate.edu/concern/honors_college_theses/9019s447b

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Attribute Name	Values
Creator	Killgore, Peter Lloyd
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.
License	All rights reserved
Resource Type	Honors College Thesis
Date Available	2015-06-01T14:19:08+00:00
Date Issued	2015-05-15
Degree Level	Bachelor's
Degree Name	Honors Bachelor of Science (H.B.S.)
Degree Field	Mathematics
Degree Grantor	Oregon State University
Commencement Year	2015
Advisor	Dray, Tevian
Non-Academic Affiliation	Oregon State University. Honors College
Urheberrechts-Erklärung	In Copyright
Publisher	Oregon State University
Peer Reviewed	No
Language	English [eng]
Replaces	http://hdl.handle.net/1957/55902

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