http://sites.science.oregonstate.edu/coursewikis/GO/ 2020-01-26T13:05:25-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/ http://sites.science.oregonstate.edu/coursewikis/GO/lib/images/favicon.ico text/html 2016-04-19T10:34:31-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/bookinfo?rev=1461087271 The Geometry of the Octonions There are precisely two further generalizations of the real and complex numbers, namely, the quaternions and the octonions. The quaternions naturally describe rotations in three dimensions, and in fact, all symmetry groups are based on one of these four number systems. This book provides an elementary introduction to the properties of the octonions, with emphasis on their geometric structure. Elementary applications covered include the rotation groups and thei… text/html 2017-08-12T10:15:47-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/errata?rev=1502558147 Errata (Last update: 8/12/17) * (ss)4.1, p.15: The assertion that $i\ell$, $j\ell$, $k\ell$ square to $-1$ does not follow from the assumptions so far. See the updates page for further discussion. * (ss)6.4, p.38: The assertion in (6.29) that $SO4^\pm\cong\SO(3)$ and in (6.32) that $\SO(3)\times\SO(3)=\SO(4)$ are only true locally, not globally. The correct assertions are that $SO4^\pm\cong\SU(2)$ and that $\SO(3)\times\SO(3)$ is the factor group of $\SO(4)$ by its reflection subgroup… text/html 2014-10-25T10:43:41-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/start?rev=1414259021 The Geometry of the Octonions This wiki contains a preliminary version of the book The Geometry of the Octonions by Tevian Dray and Corinne A. Manogue. Reading mathematics in this wiki Information about the published version of the book Table of Contents Seminar Notes (2002) text/html 2016-04-19T11:28:29-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/updates?rev=1461090509 Updates (Last update: 2/19/16) * Construction of $\OO$ Using the Cayley-Dickson process of (ss)5.1, $\OO$ is constructed from $\HH$ merely by specifying that $\ell^2=-1$; the rest of the multiplication table follows from the Cayley-Dickson product. If instead one merely specifies $\ell^2=-1$, then further assumptions are needed in order to recover the full multiplication table.