Geometry of the Octonions book:go2
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2020-01-26T13:08:03-08:00Geometry of the Octonions
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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 Systemstext/html2014-08-13T17:31:00-08:00book:go2:ch10
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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 Groupstext/html2014-08-13T17:31:00-08:00book:go2:ch11
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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 Groupstext/html2014-08-21T12:43:00-08:00book:go2:ch12
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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 Groupstext/html2014-09-03T17:21:00-08:00book:go2:ch13
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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 Groupstext/html2014-09-04T11:25:00-08:00book:go2:ch14
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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 Groupstext/html2014-09-01T22:08:00-08:00book:go2:ch15
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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 Groupstext/html2012-07-10T23:20:00-08:00book:go2:ch16
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text/html2014-08-13T17:32:00-08:00book:go2:ch2
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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 Quaternionstext/html2014-08-13T17:32:00-08:00book:go2:ch3
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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. Geometrytext/html2014-08-13T17:32:00-08:00book:go2:ch4
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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. Geometrytext/html2014-08-13T17:32:00-08:00book:go2:ch5
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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 Octonionstext/html2014-09-05T12:10:00-08:00book:go2:ch6
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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/html2014-09-05T12:09:00-08:00book:go2:ch7
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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 Groupstext/html2014-08-13T17:31:00-08:00book:go2:ch8
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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 Groupstext/html2014-09-05T12:10:00-08:00book:go2:ch9
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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
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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/html2012-07-10T20:08:00-08:00book:go2:oalg
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Subalgebras of the Split Octonionstext/html2012-07-06T07:52:00-08:00book:go2:particlesn
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A Quaternionic Description of $SO(4)$text/html2014-04-19T17:04:00-08:00book:go2:so64
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The Geometry of $\SO(6,4)$text/html2012-04-08T11:33:00-08:00book:go2:so7
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The Geometry of $SO(7)$text/html2014-04-08T11:48:00-08:00book:go2:so7o
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An Octonionic Description of $SO(7)$text/html2012-04-08T11:33:00-08:00book:go2:so8
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The Geometry of $SO(8)$text/html2014-04-08T11:48:00-08:00book:go2:so8o
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An Octonionic Description of $SO(8)$text/html2014-07-02T10:03:00-08:00book:go2:sp2
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The Geometry of $Sp(4,\RR)$text/html2014-06-24T17:41:00-08:00book:go2:sp2k
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Some Symplectic Groups over Other Division Algebrastext/html2014-07-02T10:04:00-08:00book:go2:sp3
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The Geometry of $Sp(6,\$$)$text/html2012-04-08T15:43:00-08:00book:go2:spin
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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 Groupstext/html2012-04-08T11:38:00-08:00book:go2:su2
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The Geometry of $SU(2)$text/html2012-04-08T11:39:00-08:00book:go2:su22
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The Geometry of $SU(2,2)$text/html2014-06-24T17:41:00-08:00book:go2:su2k
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Some Unitary Groups over Other Division Algebrastext/html2014-04-07T16:40:00-08:00book:go2:su2kk
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The Geometry of $SU(2,KKprimeotimesKK)$text/html2012-04-08T11:37:00-08:00book:go2:su3
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The Geometry of $SU(3)$text/html2012-04-08T11:39:00-08:00book:go2:su33
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The Geometry of $SU(3,3)$text/html2012-07-10T21:01:00-08:00book:go2:su3k
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The Geometry of $SU(3,KKprimeotimesKK)$text/html2012-07-10T22:21:00-08:00book:go2:sym
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Symplectic Transformationstext/html2014-04-19T17:00:00-08:00book:go2:u1
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The Geometry of $\Ug(1)$text/html2012-07-10T22:23:00-08:00book:go2:unitary
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Unitary Transformationstext/html2012-04-08T15:47:00-08:00book:go2:weyl
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The Weyl Equationtext/html2012-07-06T07:51:00-08:00book:go2:weyln
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The Weyl Equation