Geometry of the Octonions book:go2 http://sites.science.oregonstate.edu/coursewikis/GO/ 2020-01-26T13:08:03-08:00 Geometry of the Octonions http://sites.science.oregonstate.edu/coursewikis/GO/ http://sites.science.oregonstate.edu/coursewikis/GO/lib/images/favicon.ico text/html 2014-05-04T20:56:00-08:00 book:go2:22non http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/22non?rev=1399262160 The $2 imes2$ Non-Real Eigenvalue Problem text/html 2014-05-04T20:56:00-08:00 book:go2:22real http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/22real?rev=1399262160 The $2 imes2$ Real Eigenvalue Problem text/html 2012-07-10T20:59:00-08:00 book:go2:2square http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/2square?rev=1341979140 The $2 imes2$ Magic Square text/html 2014-05-04T20:56:00-08:00 book:go2:33non http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/33non?rev=1399262160 The $3 imes3$ Non-Real Eigenvalue Problem text/html 2014-05-04T20:56:00-08:00 book:go2:33real http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/33real?rev=1399262160 The $3 imes3$ Real Eigenvalue Problem text/html 2014-09-04T11:26:00-08:00 book:go2:3psi http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/3psi?rev=1409855160 The $3$-$\Psi$ Rule text/html 2012-07-10T20:59:00-08:00 book:go2:3square http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/3square?rev=1341979140 The $3 imes3$ Magic Square text/html 2014-07-05T13:58:00-08:00 book:go2:aa http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/aa?rev=1404593880 The Albert Algebra text/html 2012-04-08T12:35:00-08:00 book:go2:acknowledge http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/acknowledge?rev=1333913700 Acknowledgments text/html 2012-07-10T20:06:00-08:00 book:go2:calg http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/calg?rev=1341975960 Algebra text/html 2014-09-03T17:57:00-08:00 book:go2:cayley http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/cayley?rev=1409792220 Cayley Spinors text/html 2012-07-10T20:15:00-08:00 book:go2:cd http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/cd?rev=1341976500 The Cayley-Dickson Process text/html 2012-07-10T20:07:00-08:00 book:go2:cgeom http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/cgeom?rev=1341976020 Geometry text/html 2014-08-13T17:32:00-08:00 book:go2:ch1 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/ch1?rev=1407976320 Preface Acknowledgments Chapter 1: Introduction * (ss)1. Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems text/html 2014-08-13T17:31:00-08:00 book:go2:ch10 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/ch10?rev=1407976260 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems Part II: Symmetry Groups Chapter 6: Some Orthogonal Groups text/html 2014-08-13T17:31:00-08:00 book:go2:ch11 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/ch11?rev=1407976260 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems Part II: Symmetry Groups Chapter 6: Some Orthogonal Groups text/html 2014-08-21T12:43:00-08:00 book:go2:ch12 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/ch12?rev=1408650180 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems Part II: Symmetry Groups Chapter 6: Some Orthogonal Groups text/html 2014-09-03T17:21:00-08:00 book:go2:ch13 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/ch13?rev=1409790060 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems Part II: Symmetry Groups Chapter 6: Some Orthogonal Groups text/html 2014-09-04T11:25:00-08:00 book:go2:ch14 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/ch14?rev=1409855100 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems Part II: Symmetry Groups Chapter 6: Some Orthogonal Groups text/html 2014-09-01T22:08:00-08:00 book:go2:ch15 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/ch15?rev=1409634480 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems Part II: Symmetry Groups Chapter 6: Some Orthogonal Groups text/html 2012-07-10T23:20:00-08:00 book:go2:ch16 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/ch16?rev=1341987600 text/html 2014-08-13T17:32:00-08:00 book:go2:ch2 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/ch2?rev=1407976320 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers * (ss)1. Introduction * (ss)2. History * (ss)3. Algebra * (ss)4. Geometry Chapter 3: The Geometry of the Quaternions text/html 2014-08-13T17:32:00-08:00 book:go2:ch3 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/ch3?rev=1407976320 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions * (ss)1. Introduction * (ss)2. History * (ss)3. Algebra * (ss)4. Geometry text/html 2014-08-13T17:32:00-08:00 book:go2:ch4 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/ch4?rev=1407976320 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions * (ss)1. Introduction * (ss)2. History * (ss)3. Algebra * (ss)4. Geometry text/html 2014-08-13T17:32:00-08:00 book:go2:ch5 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/ch5?rev=1407976320 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems * (ss)1. The Cayley-Dickson Process * (ss)2. Sedenions * (ss)3. The Hurwitz Theorem * (ss)4. Split Complex Numbers * (ss)5. Split Quaternions * (ss)6. Split Octonions * (ss)7. Subalgebras of the Split Octonions text/html 2014-09-05T12:10:00-08:00 book:go2:ch6 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/ch6?rev=1409944200 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems Part II: Symmetry Groups Chapter 6: Some Orthogonal Groups * (ss)1. Rotations * (ss)2. The Geometry of $SO(2)$ * (ss)3. The Geometry of $SO(3)$ * (ss)4. The Geometry of $SO(4)$ * (ss)5. Lorentz Transformations * (ss)6. The Geometry of $SO(… text/html 2014-09-05T12:09:00-08:00 book:go2:ch7 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/ch7?rev=1409944140 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems Part II: Symmetry Groups Chapter 6: Some Orthogonal Groups text/html 2014-08-13T17:31:00-08:00 book:go2:ch8 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/ch8?rev=1407976260 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems Part II: Symmetry Groups Chapter 6: Some Orthogonal Groups text/html 2014-09-05T12:10:00-08:00 book:go2:ch9 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/ch9?rev=1409944200 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems Part II: Symmetry Groups Chapter 6: Some Orthogonal Groups text/html 2012-07-10T20:06:00-08:00 book:go2:chist http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/chist?rev=1341975960 History text/html 2012-04-08T15:40:00-08:00 book:go2:cintro http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/cintro?rev=1333924800 Complex Numbers text/html 2014-07-03T17:09:00-08:00 book:go2:class http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/class?rev=1404432540 The Classification of Lie Algebras text/html 2012-07-06T07:53:00-08:00 book:go2:complexn http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/complexn?rev=1341586380 Complex Numbers text/html 2012-07-10T20:16:00-08:00 book:go2:csplit http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/csplit?rev=1341976560 Split Complex Numbers text/html 2014-09-03T17:23:00-08:00 book:go2:diag http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/diag?rev=1409790180 Diagonalizing Jordan Matrices using $F_4$ text/html 2012-04-08T15:46:00-08:00 book:go2:dirac http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/dirac?rev=1333925160 Introduction to the Dirac Equation text/html 2012-07-06T07:52:00-08:00 book:go2:diracn http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/diracn?rev=1341586320 Introduction to the Dirac Equation text/html 2012-04-08T11:40:00-08:00 book:go2:e6 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/e6?rev=1333910400 The Geometry of $E_6$ text/html 2012-04-08T11:40:00-08:00 book:go2:e7 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/e7?rev=1333910400 The Geometry of $E_7$ text/html 2012-04-08T11:40:00-08:00 book:go2:e8 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/e8?rev=1333910400 The Geometry of $E_8$ text/html 2014-08-14T21:41:00-08:00 book:go2:e8latt http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/e8latt?rev=1408077660 The Geometry of the $\ee_8$ Lattice text/html 2012-04-08T15:45:00-08:00 book:go2:eigen http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/eigen?rev=1333925100 The Eigenvalue Problem text/html 2012-07-06T07:52:00-08:00 book:go2:eigenn http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/eigenn?rev=1341586320 The Eigenvalue Problem text/html 2012-04-08T11:39:00-08:00 book:go2:f4 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/f4?rev=1333910340 The Geometry of $F_4$ text/html 2012-07-10T22:19:00-08:00 book:go2:forms http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/forms?rev=1341983940 Real Forms text/html 2012-04-08T11:39:00-08:00 book:go2:g2 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/g2?rev=1333910340 The Geometry of $G_2$ text/html 2012-04-08T15:47:00-08:00 book:go2:gamma http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/gamma?rev=1333925220 Gamma Matrices text/html 2012-07-06T07:52:00-08:00 book:go2:gamman http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/gamman?rev=1341586320 Gamma Matrices text/html 2012-04-08T15:42:00-08:00 book:go2:hopf http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/hopf?rev=1333924920 The Hopf Bundles text/html 2012-07-06T07:52:00-08:00 book:go2:hopfn http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/hopfn?rev=1341586320 The Hopf Bundles text/html 2012-07-10T20:15:00-08:00 book:go2:hurwitz http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/hurwitz?rev=1341976500 The Hurwitz Theorem text/html 2012-04-08T16:04:00-08:00 book:go2:intro http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/intro?rev=1333926240 Introduction text/html 2014-09-03T17:55:00-08:00 book:go2:jnw http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/jnw?rev=1409792100 The Jordan Formulation of Quantum Mechanics text/html 2012-07-10T22:15:00-08:00 book:go2:jordan http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/jordan?rev=1341983700 The Jordan Eigenvalue Problem text/html 2012-07-10T20:41:00-08:00 book:go2:leech http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/leech?rev=1341978060 The Geometry of the Leech Lattice text/html 2012-07-10T22:03:00-08:00 book:go2:leptons http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/leptons?rev=1341982980 Leptons text/html 2012-07-10T22:19:00-08:00 book:go2:liea http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/liea?rev=1341983940 Lie Algebras text/html 2012-07-10T22:19:00-08:00 book:go2:lieg http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/lieg?rev=1341983940 Lie Groups text/html 2012-04-08T15:41:00-08:00 book:go2:lorentz http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/lorentz?rev=1333924860 Lorentz Transformations text/html 2012-07-06T07:52:00-08:00 book:go2:lorentzn http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/lorentzn?rev=1341586320 Lorentz Transformations text/html 2014-08-13T17:48:00-08:00 book:go2:mobius http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/mobius?rev=1407977280 Möbius Transformations text/html 2012-07-06T07:54:00-08:00 book:go2:notes http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/notes?rev=1341586440 These notes, coauthored with Corinne Manogue, formed the basis for formal and informal seminars at several institutions, including Mount Holyoke and Grinnell Colleges during 2002, and Oregon State University in 2004. A PDF version of these notes is available here. text/html 2012-07-10T20:08:00-08:00 book:go2:oalg http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/oalg?rev=1341976080 Algebra text/html 2012-07-06T07:52:00-08:00 book:go2:octonionsn http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/octonionsn?rev=1341586320 Octonions text/html 2012-07-10T20:08:00-08:00 book:go2:ogeom http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/ogeom?rev=1341976080 Geometry text/html 2012-07-10T20:08:00-08:00 book:go2:ohist http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/ohist?rev=1341976080 History text/html 2014-08-14T18:33:00-08:00 book:go2:oint http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/oint?rev=1408066380 Octonionic Integers text/html 2012-04-08T15:40:00-08:00 book:go2:ointro http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/ointro?rev=1333924800 Octonions text/html 2014-08-21T13:06:00-08:00 book:go2:op1 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http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/so4h?rev=1396983120 A Quaternionic Description of $SO(4)$ text/html 2014-04-19T17:04:00-08:00 book:go2:so64 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/so64?rev=1397952240 The Geometry of $\SO(6,4)$ text/html 2012-04-08T11:33:00-08:00 book:go2:so7 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/so7?rev=1333909980 The Geometry of $SO(7)$ text/html 2014-04-08T11:48:00-08:00 book:go2:so7o http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/so7o?rev=1396982880 An Octonionic Description of $SO(7)$ text/html 2012-04-08T11:33:00-08:00 book:go2:so8 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/so8?rev=1333909980 The Geometry of $SO(8)$ text/html 2014-04-08T11:48:00-08:00 book:go2:so8o http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/so8o?rev=1396982880 An Octonionic Description of $SO(8)$ text/html 2014-07-02T10:03:00-08:00 book:go2:sp2 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/sp2?rev=1404320580 The Geometry of $Sp(4,\RR)$ text/html 2014-06-24T17:41:00-08:00 book:go2:sp2k http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/sp2k?rev=1403656860 Some Symplectic Groups over Other Division Algebras text/html 2014-07-02T10:04:00-08:00 book:go2:sp3 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/sp3?rev=1404320640 The Geometry of $Sp(6,\$$)$ text/html 2012-04-08T15:43:00-08:00 book:go2:spin http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/spin?rev=1333924980 Spin text/html 2012-07-06T07:51:00-08:00 book:go2:spinn http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/spinn?rev=1341586260 Spin text/html 2012-04-08T15:42:00-08:00 book:go2:spinors http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/spinors?rev=1333924920 Spinors text/html 2012-07-06T07:51:00-08:00 book:go2:spinorsn http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/spinorsn?rev=1341586260 Spinors text/html 2014-08-13T17:32:00-08:00 book:go2:start http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/start?rev=1407976320 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems Part II: Symmetry Groups Chapter 6: Some Orthogonal Groups text/html 2012-04-08T11:38:00-08:00 book:go2:su2 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/su2?rev=1333910280 The Geometry of $SU(2)$ text/html 2012-04-08T11:39:00-08:00 book:go2:su22 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/su22?rev=1333910340 The Geometry of $SU(2,2)$ text/html 2014-06-24T17:41:00-08:00 book:go2:su2k http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/su2k?rev=1403656860 Some Unitary Groups over Other Division Algebras text/html 2014-04-07T16:40:00-08:00 book:go2:su2kk http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/su2kk?rev=1396914000 The Geometry of $SU(2,KKprimeotimesKK)$ text/html 2012-04-08T11:37:00-08:00 book:go2:su3 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/su3?rev=1333910220 The Geometry of $SU(3)$ text/html 2012-04-08T11:39:00-08:00 book:go2:su33 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/su33?rev=1333910340 The Geometry of $SU(3,3)$ text/html 2012-07-10T21:01:00-08:00 book:go2:su3k http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/su3k?rev=1341979260 text/html 2014-04-07T16:40:00-08:00 book:go2:su3kk http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/su3kk?rev=1396914000 The Geometry of $SU(3,KKprimeotimesKK)$ text/html 2012-07-10T22:21:00-08:00 book:go2:sym http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/sym?rev=1341984060 Symplectic Transformations text/html 2014-04-19T17:00:00-08:00 book:go2:u1 http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/u1?rev=1397952000 The Geometry of $\Ug(1)$ text/html 2012-07-10T22:23:00-08:00 book:go2:unitary http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/unitary?rev=1341984180 Unitary Transformations text/html 2012-04-08T15:47:00-08:00 book:go2:weyl http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/weyl?rev=1333925220 The Weyl Equation text/html 2012-07-06T07:51:00-08:00 book:go2:weyln http://sites.science.oregonstate.edu/coursewikis/GO/book/go2/weyln?rev=1341586260 The Weyl Equation